Generalizing the Singular Value Decomposition
Abstract
Two generalizations of the singular value decomposition are given. These generalizations provided a unified way of regarding certain matrix problems and the numerical techniques which are used to solve them.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
J. H. Argyris, O. E. Bronlund, The natural factor formulation of the stiffness for the matrix displacement method, Computer Methods in Applied Mechanics and Engineering, 5 (1975), 97–119
2.
Gilbert Strang, George J. Fix, An analysis of the finite element method, Prentice-Hall Inc., Englewood Cliffs, N. J., 1973xiv+306
3.
W. Morven Gentleman, Least squares computations by Givens transformations without square roots, J. Inst. Math. Appl., 12 (1973), 329–336
4.
G. H. Golub, P. Businger, An ALGOL procedure for computing the singular value decomposition, Stanford University Rep. C573, Stanford Univ., Stanford, Calif., 1967
5.
G. H. Golub, C. Reinsch, Singular value decomposition and least squares solutions, Numer. Math., 14 (1970), 403–420
6.
G. Golub, W. Kahan, Calculating the singular values and pseudo-inverse of a matrix, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 205–224
7.
Charles L. Lawson, Richard J. Hanson, Solving least squares problems, Prentice-Hall Inc., Englewood Cliffs, N.J., 1974xii+340
8.
O. Leringe, P. Wedin, A comparison between different methods to compute a vector x which minimizes |Ax−b∥2 when Gx=h, Rep., Lund University Computer Science, Lund Univ., Lund, Sweden, 1970
9.
C. B. Moler, G. W. Stewart, An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal., 10 (1973), 241–256
10.
G. W. Stewart, On the sensitivity of the eigenvalue problem $Ax=\lambda Bx$, SIAM J. Numer. Anal., 9 (1972), 669–686
11.
Charles F. Van Loan, A general matrix eigenvalue algorithm, SIAM J. Numer. Anal., 12 (1975), 819–834
12.
C. F. Van Loan, Ph.D. Thesis, Generalized singular values with algorithms and applications, University of Michigan, Ann Arbor, Michigan, 1973
Information & Authors
Information
Published In
Copyright
Copyright © 1976 Society for Industrial and Applied Mathematics.
History
Submitted: 4 October 1974
Published online: 14 July 2006
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Tensor Decompositions: Principles and Application to Food SciencesSource Separation in Physical‐Chemical Sensing | 13 October 2023
- Earthquake Forecasting Using Big Data and Artificial Intelligence: A 30-Week Real-Time Case Study in ChinaBulletin of the Seismological Society of America, Vol. 113, No. 6 | 5 September 2023
- Explainable, Stable, and Scalable Network Embedding Algorithms for Unsupervised Learning of Graph RepresentationsIEEE Transactions on Computational Social Systems, Vol. 10, No. 5 | 1 Oct 2023
- Towards precise complex AM-FM signals decomposition under strong noise conditions: A novel two-level chirp mode decomposition approachMechanical Systems and Signal Processing, Vol. 200 | 1 Oct 2023
- Kernel-based PMP structure for nonlinear industrial quality-related process monitoringISA Transactions, Vol. 141 | 1 Oct 2023
- A Higher-Order Generalized Singular Value Decomposition for Rank-Deficient MatricesSIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 3 | 21 July 2023
- Principal Components Along Quiver RepresentationsFoundations of Computational Mathematics, Vol. 23, No. 4 | 29 April 2022
- Thick-restarted joint Lanczos bidiagonalization for the GSVDJournal of Computational and Applied Mathematics, Vol. 13 | 1 Aug 2023
- CasTensoRF: Cascaded Tensorial Radiance Fields for Novel View Synthesis2023 IEEE International Conference on Multimedia and Expo (ICME) | 1 Jul 2023
- MIMO Radar Transmit Signal Optimization for Target Localization Exploiting Prior Information2023 IEEE International Symposium on Information Theory (ISIT) | 25 Jun 2023
- Rate Splitting and Precoding Strategies for Multi-User MIMO Broadcast Channels with Common and Private StreamsICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) | 4 Jun 2023
- Merging three‐dimensional occupancy grid maps to support multi‐UAVs cooperative navigation systemsJournal of Field Robotics, Vol. 40, No. 3 | 9 December 2022
- Matrix denoising with partial noise statistics: optimal singular value shrinkage of spiked F-matricesInformation and Inference: A Journal of the IMA, Vol. 12, No. 3 | 11 July 2023
- A regularity augmented evolutionary algorithm with dual-space search for multiobjective optimizationSwarm and Evolutionary Computation, Vol. 78 | 1 Apr 2023
- A projection continuation approach for minimal coordinate set constrained dynamicsMultibody System Dynamics, Vol. 57, No. 3-4 | 7 February 2023
- The Joint Bidiagonalization Method for Large GSVD Computations in Finite PrecisionSIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 1 | 17 March 2023
- Machine learning brings new insights for reducing salinization disasterFrontiers in Earth Science, Vol. 11 | 9 February 2023
- Stabilization of Generalized Empirical Interpolation Method (GEIM) in presence of noise: A novel approach based on Tikhonov regularizationComputer Methods in Applied Mechanics and Engineering, Vol. 404 | 1 Feb 2023
- Optical double-image cryptosystem based on generalized singular value decomposition and five-dimensional hyperchaotic mapsApplied Optics, Vol. 62, No. 3 | 13 January 2023
- Model order reduction techniques to identify submarining risk in a simplified human body modelComputer Methods in Biomechanics and Biomedical Engineering, Vol. 78 | 10 January 2023
- Weighted Least Squares Perturbation TheoryMatrix Theory - Classics and Advances | 4 January 2023
- Long-Range Non-Line-of-Sight Imaging Based on Projected Images from Multiple Light FieldsPhotonics, Vol. 10, No. 1 | 26 December 2022
- A Cross-Product Free Jacobi–Davidson Type Method for Computing a Partial Generalized Singular Value Decomposition of a Large Matrix PairJournal of Scientific Computing, Vol. 94, No. 1 | 23 November 2022
- A New Visual and Inertial and Satellite Integrated Navigation Method Based on Point Cloud RegistrationAdvances in Natural Computation, Fuzzy Systems and Knowledge Discovery | 30 January 2023
- Exercise recommendation method based on knowledge tracing and concept prerequisite relationsCCF Transactions on Pervasive Computing and Interaction, Vol. 4, No. 4 | 28 June 2022
- Sequence neural network for recommendation with multi-feature fusionExpert Systems with Applications, Vol. 210 | 1 Dec 2022
- Two Harmonic Jacobi–Davidson Methods for Computing a Partial Generalized Singular Value Decomposition of a Large Matrix PairJournal of Scientific Computing, Vol. 93, No. 2 | 16 September 2022
- Generalized orthogonalization: a unified framework for Gram–Schmidt orthogonalization, SVD and PCA2022 IEEE International Conference on Systems, Man, and Cybernetics (SMC) | 9 Oct 2022
- An investigation of the thermal behavior of constructal theory-based pore-scale porous media by using a combination of computational fluid dynamics and machine learningInternational Journal of Heat and Mass Transfer, Vol. 194 | 1 Sep 2022
- Non-destructive online seal integrity inspection utilizing autoencoder-based electrical capacitance tomography for product packaging assuranceFood Packaging and Shelf Life, Vol. 33 | 1 Sep 2022
- 2D Phase-Based RFID Localization for On-Site Landslide MonitoringRemote Sensing, Vol. 14, No. 15 | 26 July 2022
- A novel macro-scale machine learning prediction based on high-fidelity CFD simulations: A case study on the pore-scale porous Trombe wall with phase change material capsulationJournal of Building Engineering, Vol. 54 | 1 Aug 2022
- Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix PairSIAM Journal on Matrix Analysis and Applications, Vol. 43, No. 2 | 5 April 2022
- On the Cartan decomposition for classical random matrix ensemblesJournal of Mathematical Physics, Vol. 63, No. 6 | 15 June 2022
- Precoding and Decoding Schemes for Downlink MIMO-RSMA with Simultaneous Diagonalization and User Exclusion2022 IEEE International Conference on Communications Workshops (ICC Workshops) | 16 May 2022
- ReferencesMultiblock Data Fusion in Statistics and Machine Learning | 15 April 2022
- A Generalized CUR Decomposition for Matrix PairsSIAM Journal on Mathematics of Data Science, Vol. 4, No. 1 | 17 March 2022
- Solar Power ForecastsComprehensive Renewable Energy | 1 Jan 2022
- User-Heterogeneous Cell-Free Massive MIMO Downlink and Uplink Beamforming via Tensor DecompositionIEEE Open Journal of the Communications Society, Vol. 3 | 1 Jan 2022
- Multilinear Generalized Singular Value Decomposition (ML-GSVD) and Its Application to Multiuser MIMO SystemsIEEE Transactions on Signal Processing, Vol. 70 | 1 Jan 2022
- Analytical solutions of a class of matrix function optimization problems with unitary constraintsApplied Mathematics Letters, Vol. 123 | 1 Jan 2022
- Weighted generalized tensor functions based on the tensor-product and their applicationsFilomat, Vol. 36, No. 18 | 1 Jan 2022
- Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical TomographyDüzce Üniversitesi Bilim ve Teknoloji Dergisi | 31 December 2021
- Learning Latent Variable Models with Regularization2021 International Conference on Electrical, Computer and Energy Technologies (ICECET) | 9 Dec 2021
- A Comparative Study of Fuzzy Topic Models and LDA in terms of Interpretability2021 IEEE Symposium Series on Computational Intelligence (SSCI) | 5 Dec 2021
- Quantum Machine Learning for Electricity Theft Detection: an Initial Investigation2021 IEEE International Conferences on Internet of Things (iThings) and IEEE Green Computing & Communications (GreenCom) and IEEE Cyber, Physical & Social Computing (CPSCom) and IEEE Smart Data (SmartData) and IEEE Congress on Cybermatics (Cybermatics) | 1 Dec 2021
- Multiblock variable influence on orthogonal projections (MB-VIOP) for enhanced interpretation of total, global, local and unique variations in OnPLS modelsBMC Bioinformatics, Vol. 22, No. 1 | 3 April 2021
- Spherical harmonic covariance and magnitude function encodings for beamformer designEURASIP Journal on Audio, Speech, and Music Processing, Vol. 2021, No. 1 | 3 December 2021
- PyParSVD: A streaming, distributed and randomized singular-value-decomposition library2021 7th International Workshop on Data Analysis and Reduction for Big Scientific Data (DRBSD-7) | 1 Nov 2021
- The joint bidiagonalization process with partial reorthogonalizationNumerical Algorithms, Vol. 88, No. 2 | 26 January 2021
- Optical Fiber Ball Resonator Sensor Spectral Interrogation through Undersampled KLT: Application to Refractive Index Sensing and Cancer Biomarker BiosensingSensors, Vol. 21, No. 20 | 10 October 2021
- Some applications of a decomposition for five quaternion matrices in control system and color image processingComputational and Applied Mathematics, Vol. 40, No. 6 | 11 August 2021
- Moving load identification on Euler-Bernoulli beams with viscoelastic boundary conditions by Tikhonov regularizationInverse Problems in Science and Engineering, Vol. 29, No. 8 | 8 September 2020
- Dynamics of interaction between an Euler-Bernoulli beam and a moving damped sprung mass: Effect of beam surface roughnessStructures, Vol. 32 | 1 Aug 2021
- Influences of Elastic Supports on Moving Load Identification of Euler–Bernoulli Beams Using Angular VelocityJournal of Vibration and Acoustics, Vol. 143, No. 4 | 8 December 2020
- Randomized algorithms for generalized singular value decomposition with application to sensitivity analysisNumerical Linear Algebra with Applications, Vol. 28, No. 4 | 24 February 2021
- Unsupervised Learning in Accordance With New Aspects of Artificial IntelligenceMachine Learning Approach for Cloud Data Analytics in IoT | 3 August 2021
- Model reduction techniques for quantitative nano-mechanical AFM modeMeasurement Science and Technology, Vol. 32, No. 7 | 10 May 2021
- On choices of formulations of computing the generalized singular value decomposition of a large matrix pairNumerical Algorithms, Vol. 87, No. 2 | 7 August 2020
- On Learning the Geodesic Path for Incremental Learning2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) | 1 Jun 2021
- A deconvolution method for signal recovery of electromagnetic field sensorsMeasurement, Vol. 178 | 1 Jun 2021
- Linear Algebra, ComputationalWiley StatsRef: Statistics Reference Online | 17 May 2021
- Iterative Methods to Calculate Weighted Pseudoinverses with Mixed WeightsCybernetics and Systems Analysis, Vol. 57, No. 3 | 27 May 2021
- Optimal Spectral Shrinkage and PCA With Heteroscedastic NoiseIEEE Transactions on Information Theory, Vol. 67, No. 5 | 1 May 2021
- On worst-case condition numbers of a multiple nonzero finite generalized singular valueLinear Algebra and its Applications, Vol. 616 | 1 May 2021
- Condition numbers for the K -weighted pseudoinverse and their statistical estimationLinear and Multilinear Algebra, Vol. 69, No. 4 | 20 May 2019
- Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matricesSeMA Journal, Vol. 78, No. 1 | 30 August 2020
- Randomized Generalized Singular Value DecompositionCommunications on Applied Mathematics and Computation, Vol. 3, No. 1 | 7 March 2020
- Implicit Hari–Zimmermann algorithm for the generalized SVD on the GPUsThe International Journal of High Performance Computing Applications, Vol. 35, No. 2 | 10 December 2020
- Detecting and Locating Passive Video Forgery Based on Low Computational Complexity Third-Order Tensor RepresentationJournal of Imaging, Vol. 7, No. 3 | 5 March 2021
- Shear Wave Dispersion as a Potential Biomarker for Cervical Remodeling During Pregnancy: Evidence From a Non-Human Primate ModelFrontiers in Physics, Vol. 8 | 15 February 2021
- Covariance NMR: Theoretical concerns, practical considerations, contemporary applications and related techniquesProgress in Nuclear Magnetic Resonance Spectroscopy, Vol. 122 | 1 Feb 2021
- A study of the family service expenditures and the socio-demographic characteristics via fixed marginals correspondence analysisSocio-Economic Planning Sciences, Vol. 73 | 1 Feb 2021
- Precoder Design and Statistical Power Allocation for MIMO-NOMA via User-Assisted Simultaneous DiagonalizationIEEE Transactions on Communications, Vol. 69, No. 2 | 1 Feb 2021
- A Preliminary Work: Mixed Reality-Integrated Computer-Aided Surgical Navigation System for Paranasal Sinus Surgery Using Microsoft HoloLens 2Advances in Computer Graphics | 11 October 2021
- Understanding Ethereum Transactions via Network ApproachGraph Data Mining | 26 April 2021
- Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO ChannelsIEEE Transactions on Signal Processing, Vol. 69 | 1 Jan 2021
- Improvement of deep cross-modal retrieval by generating real-valued representationPeerJ Computer Science, Vol. 7 | 27 April 2021
- Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulenceJournal of Computational Physics, Vol. 419 | 1 Oct 2020
- Point data reconstruction and smoothing using cubic splines and clusterizationMathematics and Computers in Simulation, Vol. 176 | 1 Oct 2020
- A Generalized-SVD-Based Technique for Enhancing Performance of Multi-Temporal Dinsar Analyses: The Weighted Adaptive Variable-Length (Wave) TechniqueIGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Symposium | 26 Sep 2020
- FRET-enhanced photoluminescence of perylene diimides by combining molecular aggregation and insulationJournal of Materials Chemistry C, Vol. 8, No. 26 | 1 January 2020
- An extension of analytic solutions of a class of constrained matrix minimization problemsJournal of Computational and Applied Mathematics, Vol. 372 | 1 Jul 2020
- Overview and comparative study of dimensionality reduction techniques for high dimensional dataInformation Fusion, Vol. 59 | 1 Jul 2020
- Iterative Solution of Weighted Linear Least Squares ProblemsAnalele Universitatii "Ovidius" Constanta - Seria Matematica, Vol. 28, No. 2 | 22 September 2020
- Existence and Uniqueness of Weighted Pseudoinverses with Nonsingular Indefinite WeightsCybernetics and Systems Analysis, Vol. 56, No. 3 | 25 May 2020
- Analytic solutions of a class of extended constrained matrix maximization problemsApplied Mathematics and Computation, Vol. 372 | 1 May 2020
- Multilinear Generalized Singular Value Decomposition (Ml-gsvd) with Application to Coordinated Beamforming in Multi-user Mimo SystemsICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) | 1 May 2020
- Problems of Improving the Diagnostic Systems of Marine Diesel Generator Sets2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET) | 1 Feb 2020
- On the Use of Weighted Least-Squares Approaches for Differential Interferometric SAR Analyses: The Weighted Adaptive Variable-lEngth (WAVE) TechniqueSensors, Vol. 20, No. 4 | 18 February 2020
- The GSVD: Where are the Ellipses?, Matrix Trigonometry, and MoreSIAM Journal on Matrix Analysis and Applications, Vol. 41, No. 4 | 24 November 2020
- Neural NetworksTheory and Computation of Complex Tensors and its Applications | 2 April 2020
- Community detection in Networks using Graph EmbeddingProcedia Computer Science, Vol. 173 | 1 Jan 2020
- An efficient hyperpower iterative method for computing weighted MoorePenrose inverseAIMS Mathematics, Vol. 5, No. 3 | 1 Jan 2020
- 110th Anniversary: Generalized Singular Value Decomposition Reduced-Order Observers for Linear Time-Invariant Systems with Noisy MeasurementsIndustrial & Engineering Chemistry Research, Vol. 58, No. 51 | 17 October 2019
- Forecasting Causes of Death by Using Compositional Data Analysis: The Case of Cancer DeathsJournal of the Royal Statistical Society Series C: Applied Statistics, Vol. 68, No. 5 | 13 June 2019
- Expansions of Weighted Pseudoinverses with Mixed Weights into Matrix Power Series and Power ProductsCybernetics and Systems Analysis, Vol. 55, No. 5 | 18 October 2019
- Properties of subgradient projection iteration when applying to linear imaging systemOptimization Letters, Vol. 13, No. 6 | 30 August 2018
- Active learning to detect DDoS attack using ranked featuresComputer Communications, Vol. 145 | 1 Sep 2019
- Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration SchemeMathematics, Vol. 7, No. 8 | 10 August 2019
- Downlink Precoder Design for Two-User Power-Domain MIMO-NOMA with Excess Degrees of Freedom2019 IEEE International Conference on Communications Workshops (ICC Workshops) | 1 May 2019
- Comparison and evaluation of integrative methods for the analysis of multilevel omics data: a study based on simulated and experimental cancer dataBriefings in Bioinformatics, Vol. 20, No. 2 | 23 April 2018
- An analytical method for measuring the Parkinson’s disease progression: A case on a Parkinson’s telemonitoring datasetMeasurement, Vol. 136 | 1 Mar 2019
- Convergence in Norm of Nonsymmetric Algebraic MultigridSIAM Journal on Scientific Computing, Vol. 41, No. 5 | 29 October 2019
- Tikhonov RegularizationParameter Estimation and Inverse Problems | 1 Jan 2019
- BibliographyParameter Estimation and Inverse Problems | 1 Jan 2019
- Distribution of relaxation times investigation of $$\hbox {Co}^{3+}$$ Co 3 + doping lithium-rich cathode material $$\hbox {Li}[\hbox {Li}_{0.2} \hbox {Ni}_{0.1} \hbox {Mn}_{0.5} \hbox {Co}_{0.2}]\hbox {O}_{2}$$ Li [ Li 0.2 Ni 0.1 Mn 0.5 Co 0.2 ] O 2Bulletin of Materials Science, Vol. 41, No. 6 | 5 December 2018
- OnPLS-Based Multi-Block Data Integration: A Multivariate Approach to Interrogating Biological Interactions in AsthmaAnalytical Chemistry, Vol. 90, No. 22 | 18 October 2018
- Explicit determinantal representation formulas for the solution of the two-sided restricted quaternionic matrix equationJournal of Applied Mathematics and Computing, Vol. 58, No. 1-2 | 2 November 2017
- Mathematically universal and biologically consistent astrocytoma genotype encodes for transformation and predicts survival phenotypeAPL Bioengineering, Vol. 2, No. 3 | 19 September 2018
- Graph embedding techniques, applications, and performance: A surveyKnowledge-Based Systems, Vol. 151 | 1 Jul 2018
- An interval extension of SMS method for computing weighted Moore–Penrose inverseCalcolo, Vol. 55, No. 2 | 15 March 2018
- Acute perturbation bounds of weighted Moore–Penrose inverseInternational Journal of Computer Mathematics, Vol. 95, No. 4 | 6 March 2017
- Kernel-penalized regression for analysis of microbiome dataThe Annals of Applied Statistics, Vol. 12, No. 1 | 1 Mar 2018
- The MIMO Wiretap Channel DecomposedIEEE Transactions on Information Theory, Vol. 64, No. 2 | 1 Feb 2018
- Controllability radii of linear neutral systems under structured perturbationsInternational Journal of Control, Vol. 91, No. 1 | 3 January 2017
- The complete equivalence canonical form of four matrices over an arbitrary division ringLinear and Multilinear Algebra, Vol. 66, No. 1 | 31 January 2017
- Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLSSIAM Review, Vol. 60, No. 2 | 8 May 2018
- The Discrete Empirical Interpolation Method: Canonical Structure and Formulation in Weighted Inner Product SpacesSIAM Journal on Matrix Analysis and Applications, Vol. 39, No. 3 | 12 July 2018
- On the Explicit Expression of Chordal Metric between Generalized Singular Values of Grassmann Matrix Pairs with ApplicationsSIAM Journal on Matrix Analysis and Applications, Vol. 39, No. 4 | 11 October 2018
- Data Driven Modal Decompositions: Analysis and EnhancementsSIAM Journal on Scientific Computing, Vol. 40, No. 4 | 17 July 2018
- Matrix DecompositionEncyclopedia of Social Network Analysis and Mining | 12 June 2018
- Computational AspectsGeneralized Inverses: Theory and Computations | 13 May 2018
- Secure and Robust Fragile Watermarking Scheme for Medical ImagesIEEE Access, Vol. 6 | 1 Jan 2018
- A weighted singular value decomposition for the discrete inverse problemsNumerical Linear Algebra with Applications, Vol. 25, No. 1 | 6 August 2017
- Partial condition number for the equality constrained linear least squares problemCalcolo, Vol. 54, No. 4 | 7 April 2017
- Neural networks for computing best rank-one approximations of tensors and its applicationsNeurocomputing, Vol. 267 | 1 Dec 2017
- Sliding mode fault‐tolerant control of uncertain system: A delta operator approachInternational Journal of Robust and Nonlinear Control, Vol. 27, No. 18 | 22 February 2017
- Semantic Search-by-Examples for Scientific Topic Corpus Expansion in Digital Libraries2017 IEEE International Conference on Data Mining Workshops (ICDMW) | 1 Nov 2017
- A Generalized Singular Value Decomposition Strategy for Estimating the Block Recursive Simultaneous Equations ModelComputational Economics, Vol. 50, No. 3 | 9 June 2016
- Constrained Dynamic Systems: Generalized Modeling and State EstimationIEEE Transactions on Aerospace and Electronic Systems, Vol. 53, No. 5 | 1 Oct 2017
- Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverseApplied Mathematics and Computation, Vol. 309 | 1 Sep 2017
- Neumann problems of 2D Laplace's equation by method of fundamental solutionsApplied Numerical Mathematics, Vol. 119 | 1 Sep 2017
- Statistical data integration: Challenges and opportunitiesStatistical Modelling, Vol. 17, No. 4-5 | 25 September 2017
- Common and distinct components in data fusionJournal of Chemometrics, Vol. 31, No. 7 | 31 May 2017
- Optimization methods for regularization-based ill-posed problems: a survey and a multi-objective frameworkFrontiers of Computer Science, Vol. 11, No. 3 | 21 June 2017
- Penalized Versus Constrained Generalized Eigenvalue ProblemsJournal of Computational and Graphical Statistics, Vol. 26, No. 2 | 24 April 2017
- Simultaneous decomposition of quaternion matrices involving η-Hermicity with applicationsApplied Mathematics and Computation, Vol. 298 | 1 Apr 2017
- Efficient Simultaneous Reconstruction of Time-Varying Images and Electrode Contact Impedances in Electrical Impedance TomographyIEEE Transactions on Biomedical Engineering, Vol. 64, No. 4 | 1 Apr 2017
- Contextualized Latent Semantic Indexing: A New Approach to Automated Chinese Essay ScoringJournal of Intelligent Systems, Vol. 26, No. 2 | 1 Apr 2017
- Blind source separation using joint canonical decomposition of two higher order tensors2017 51st Annual Conference on Information Sciences and Systems (CISS) | 1 Mar 2017
- Numerical Computation of Weil--Peterson Geodesics in the Universal Teichmüller SpaceSIAM Journal on Imaging Sciences, Vol. 10, No. 3 | 17 August 2017
- Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse ProblemsSIAM Journal on Scientific Computing, Vol. 39, No. 5 | 26 October 2017
- Goal-Oriented Optimal Approximations of Bayesian Linear Inverse ProblemsSIAM Journal on Scientific Computing, Vol. 39, No. 5 | 26 October 2017
- The Dirty MIMO Multiple-Access ChannelIEEE Transactions on Information Theory, Vol. e 63 | 1 Jan 2017
- On the ergodic secrecy capacity and secrecy outage probability of the MIMOME Rayleigh wiretap channelTransactions on Emerging Telecommunications Technologies, Vol. 28, No. 1 | 12 February 2015
- Structured condition numbers of structured Tikhonov regularization problem and their estimationsJournal of Computational and Applied Mathematics, Vol. 308 | 1 Dec 2016
- Recurrent neural network for computation of generalized eigenvalue problem with real diagonalizable matrix pair and its applicationsNeurocomputing, Vol. 216 | 1 Dec 2016
- Pinsker estimators for local helioseismology: inversion of travel times for mass-conserving flowsInverse Problems, Vol. 32, No. 10 | 5 August 2016
- Weighted Pseudoinversion with Singular WeightsCybernetics and Systems Analysis, Vol. 52, No. 5 | 24 September 2016
- Extensions of principle component analysis with applications on vision based computingMultimedia Tools and Applications, Vol. 75, No. 17 | 3 November 2015
- DoF region for two-cell multiuser MIMO uplink channels2016 IEEE 17th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) | 1 Jul 2016
- Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matricesLinear Algebra and its Applications, Vol. 496 | 1 May 2016
- Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen–Loève expansionNumerical Linear Algebra with Applications, Vol. 23, No. 2 | 13 November 2015
- Controllability Radii of Linear Systems with Constrained Controls Under Structured PerturbationsSIAM Journal on Control and Optimization, Vol. 54, No. 5 | 19 October 2016
- Generalizing the GSVDSIAM Journal on Numerical Analysis, Vol. 54, No. 4 | 18 August 2016
- Rank Decisions in Matrix Quotient DecompositionsSIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 4 | 14 December 2016
- A flexible condition number for weighted linear least squares problem and its statistical estimationJournal of Computational and Applied Mathematics, Vol. 292 | 1 Jan 2016
- Matrix DecompositionEncyclopedia of Social Network Analysis and Mining | 11 January 2017
- The determination of floatability distribution from laboratory batch cell testsMinerals Engineering, Vol. 83 | 1 Nov 2015
- Blocking and parallelization of the Hari–Zimmermann variant of the Falk–Langemeyer algorithm for the generalized SVDParallel Computing, Vol. 49 | 1 Nov 2015
- Radius of approximate controllability of linear retarded systems under structured perturbationsSystems & Control Letters, Vol. 84 | 1 Oct 2015
- Quantum XOR GamesACM Transactions on Computation Theory, Vol. 7, No. 4 | 31 August 2015
- Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrixComputers & Mathematics with Applications, Vol. 70, No. 5 | 1 Sep 2015
- Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular WeightsUkrainian Mathematical Journal, Vol. 67, No. 3 | 27 October 2015
- Weighted Singular Value Decomposition of Matrices with Singular Weights Based on Weighted Orthogonal TransformationsCybernetics and Systems Analysis, Vol. 51, No. 4 | 28 July 2015
- The confidential MIMO broadcast capacity: A simple derivation2015 IEEE International Symposium on Information Theory (ISIT) | 1 Jun 2015
- Joint Unitary Triangularization for Gaussian Multi-User MIMO NetworksIEEE Transactions on Information Theory, Vol. 61, No. 5 | 1 May 2015
- Anisotropic smoothing splines in problems with factorial design of experimentsDoklady Mathematics, Vol. 91, No. 2 | 30 May 2015
- Optimal Low-rank Approximations of Bayesian Linear Inverse ProblemsSIAM Journal on Scientific Computing, Vol. 37, No. 6 | 3 November 2015
- Energy-Efficient User-State Recognition Method Using Wavelet Transform and Singular Value DecompositionSICE Journal of Control, Measurement, and System Integration, Vol. 8, No. 1 | 18 January 2021
- Matrix Eigenvalue ProblemsNumerical Methods in Matrix Computations | 7 October 2014
- Multiplicative perturbation bounds for weighted polar decompositionCalcolo, Vol. 51, No. 4 | 10 October 2013
- Refining bimodal microstructure of materials with MSTRUCTPowder Diffraction, Vol. 29, No. S2 | 15 October 2014
- Verified bounds for all the singular values of matrixJapan Journal of Industrial and Applied Mathematics, Vol. 31, No. 3 | 17 May 2014
- Methods of decompositionCorrespondence Analysis | 29 August 2014
- Linear Algebra, ComputationalWiley StatsRef: Statistics Reference Online | 29 September 2014
- Infinite Vector Decomposition in Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) Perspective2014 International Conference on Mathematics and Computers in Sciences and in Industry | 1 Sep 2014
- Computation of the Real Controllability Radius and Minimum-Norm Perturbations of Higher-Order, Descriptor, and Time-Delay LTI SystemsIEEE Transactions on Automatic Control, Vol. 59, No. 8 | 1 Aug 2014
- Some new perturbation bounds of generalized polar decompositionApplied Mathematics and Computation, Vol. 233 | 1 May 2014
- Joint Space Decomposition-and-Synthesis Approach and Achievable DoF Regions for $K$-User MIMO Interference ChannelsIEEE Transactions on Signal Processing, Vol. 62, No. 9 | 1 May 2014
- On the extension of Householder’s method for weighted Moore–Penrose inverseApplied Mathematics and Computation, Vol. 231 | 1 Mar 2014
- A generalized formulation for harmonic retrieval in correlated noise2014 48th Annual Conference on Information Sciences and Systems (CISS) | 1 Mar 2014
- Necessary and sufficient conditions for the existence of a weighted singular value decomposition of matrices with singular weightsDoklady Mathematics, Vol. 89, No. 2 | 3 May 2014
- Matrix DecompositionEncyclopedia of Social Network Analysis and Mining | 5 October 2014
- “Sphere to Cylinder”: Oblique AspectMap Projections | 4 June 2014
- “Ellipsoid-of-Revolution to Cylinder”: Transverse AspectMap Projections | 4 June 2014
- Map Projections of Alternative Structures: Torus, Hyperboloid, Paraboloid, Onion Shape and OthersMap Projections | 4 June 2014
- An efficient matrix iteration for computing weighted Moore–Penrose inverseApplied Mathematics and Computation, Vol. 226 | 1 Jan 2014
- Reconstruction of the primordial power spectrum of curvature perturbations using multiple data setsJournal of Cosmology and Astroparticle Physics, Vol. 2014, No. 01 | 15 January 2014
- Optimal Spatial Matrix Filter Design for Array Signal PreprocessingJournal of Applied Mathematics, Vol. 2014 | 1 Jan 2014
- “Sphere to Cylinder”: Transverse AspectMap Projections | 4 June 2014
- “Sphere to Tangential Plane”: Oblique AspectMap Projections | 4 June 2014
- Secrecy Precoding and Beamforming in Multi-Antenna Wireless SystemsSignal Processing Approaches to Secure Physical Layer Communications in Multi-Antenna Wireless Systems | 27 September 2013
- “Sphere to Cylinder”: Polar AspectMap Projections | 4 June 2014
- “Ellipsoid-of-Revolution to Cylinder”: Oblique AspectMap Projections | 4 June 2014
- “Sphere to Cylinder”: Pseudo-Cylindrical ProjectionsMap Projections | 4 June 2014
- “Ellipsoid-of-Revolution to Cylinder”: Polar AspectMap Projections | 4 June 2014
- Ellipsoid-of-Revolution to Sphere and from Sphere to PlaneMap Projections | 4 June 2014
- Ellipsoid-of-Revolution to Tangential PlaneMap Projections | 4 June 2014
- C 10(3): The Ten Parameter Conformal Group as a Datum Transformation in Three-Dimensional Euclidean SpaceMap Projections | 4 June 2014
- Optimal Map Projections by Variational Calculus: Harmonic MapsMap Projections | 4 June 2014
- Matrix Perturbation TheoryHandbook of Linear Algebra, Second Edition | 26 November 2013
- On the computation of weighted Moore–Penrose inverse using a high-order matrix methodComputers & Mathematics with Applications, Vol. 66, No. 11 | 1 Dec 2013
- MIMO Broadcast DFE Transceivers With QoS Constraints: Min-Power and Max-Rate SolutionsIEEE Transactions on Signal Processing, Vol. 61, No. 22 | 1 Nov 2013
- An accelerated iterative method for computing weighted Moore–Penrose inverseApplied Mathematics and Computation, Vol. 222 | 1 Oct 2013
- Monitoring a 5MW offshore wind energy converter—Condition parameters and triangulation based extraction of modal parametersMechanical Systems and Signal Processing, Vol. 40, No. 1 | 1 Oct 2013
- A novel square-root Nyquist filter design with prescribed ISI energySignal Processing, Vol. 93, No. 9 | 1 Sep 2013
- An MMSE Based Signal to Leakage Plus Noise Ratio Precoding Scheme with Other Cell Interference2013 IEEE 78th Vehicular Technology Conference (VTC Fall) | 1 Sep 2013
- GSVD Beamforming for Two-User MIMO Downlink ChannelIEEE Transactions on Vehicular Technology, Vol. 62, No. 6 | 1 Jul 2013
- Exploiting fisher and fukunaga-koontz transforms in chernoff dimensionality reductionACM Transactions on Knowledge Discovery from Data, Vol. 7, No. 2 | 2 August 2013
- Common and Cluster-Specific Simultaneous Component AnalysisPLoS ONE, Vol. 8, No. 5 | 8 May 2013
- Full Rank Solutions for the MIMO Gaussian Wiretap Channel With an Average Power ConstraintIEEE Transactions on Signal Processing, Vol. 61, No. 10 | 1 May 2013
- A note on simple nonzero finite generalized singular valuesLinear Algebra and its Applications, Vol. 438, No. 8 | 1 Apr 2013
- Divide and Conquer the CS DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 2 | 25 April 2013
- BibliographyParameter Estimation and Inverse Problems | 1 Jan 2013
- Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski SpaceThe Scientific World Journal, Vol. 2013 | 1 Jan 2013
- Hermitian‐type generalized singular value decomposition with applicationsNumerical Linear Algebra with Applications, Vol. 20, No. 1 | 17 January 2012
- Sensitivity analysis for the generalized singular value decompositionNumerical Linear Algebra with Applications, Vol. 20, No. 1 | 23 February 2012
- Max-rate MIMO broadcast DFE transceiver design under power and SER constraints2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR) | 1 Nov 2012
- MIMO broadcast DFE transceiver design with bit allocation under QoS constraints2012 IEEE Statistical Signal Processing Workshop (SSP) | 1 Aug 2012
- A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with ApplicationsCommunications in Algebra, Vol. 40, No. 7 | 1 Jul 2012
- Joint MAX-SER-minimized DFE transceiver design with bit allocation for broadcast channels2012 IEEE International Conference on Communications (ICC) | 1 Jun 2012
- DISCO-SCA and Properly Applied GSVD as Swinging Methods to Find Common and Distinctive ProcessesPLoS ONE, Vol. 7, No. 5 | 31 May 2012
- New Interference Suppression Precoding Scheme for Downlink Multi-User Multi-Stream MIMO Systems2012 IEEE 75th Vehicular Technology Conference (VTC Spring) | 1 May 2012
- Solving Ill-Posed Linear Systems with GMRES and a Singular PreconditionerSIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 4 | 13 December 2012
- Effective condition number for weighted linear least squares problems and applications to the Trefftz methodEngineering Analysis with Boundary Elements, Vol. 36, No. 1 | 1 Jan 2012
- Joint Unitary Triangularization for MIMO NetworksIEEE Transactions on Signal Processing, Vol. 60, No. 1 | 1 Jan 2012
- A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple OrganismsPLoS ONE, Vol. 6, No. 12 | 22 December 2011
- The inverse problem of bimorph mirror tuning on a beamlineJournal of Synchrotron Radiation, Vol. 18, No. 6 | 30 September 2011
- An analytic approach to the problem of separability of quantum states based upon the theory of conesQuantum Information Processing, Vol. 10, No. 5 | 25 December 2010
- Physical-layer MIMO relaying2011 IEEE International Symposium on Information Theory Proceedings | 1 Jul 2011
- An equivalence canonical form of a matrix triplet over an arbitrary division ring with applicationsScience China Mathematics, Vol. 54, No. 5 | 8 January 2011
- Simultaneous SDR optimality via a joint matrix decomposition2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) | 1 May 2011
- Achieving higher uplink performance and capacity via non-overlapping window adaptive maximum noise fraction beamforming techniqueIET Communications, Vol. 5, No. 5 | 25 Mar 2011
- Reduced Order Models Using Generalized EigenanalysisProceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 225, No. 1 | 25 January 2011
- Fast Sparse Cholesky Decomposition and Inversion using Nested Dissection Matrix ReorderingJournal of Chemical Theory and Computation, Vol. 7, No. 2 | 10 January 2011
- Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problemsNumerical Linear Algebra with Applications, Vol. 18, No. 1 | 4 February 2010
- An Online Human Activity Recognizer for Mobile Phones with AccelerometerNeural Information Processing | 1 Jan 2011
- Generalized nonlinear discriminant analysis and its small sample size problemsNeurocomputing, Vol. 74, No. 4 | 1 Jan 2011
- Real controllability radius of higher-order, descriptor, and time-delay LTI systemsIFAC Proceedings Volumes, Vol. 44, No. 1 | 1 Jan 2011
- Generalized Singular Value Decomposition for Coordinated Beamforming in MIMO Systems2010 IEEE Global Telecommunications Conference GLOBECOM 2010 | 1 Dec 2010
- Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap ChannelIEEE Transactions on Information Theory, Vol. 56, No. 11 | 1 Nov 2010
- Linear mapping function to the influence of non-invasive ICP assessmentJOURNAL OF ELECTRONIC MEASUREMENT AND INSTRUMENT, Vol. 24, No. 8 | 10 Sep 2010
- Decomposing the MIMO broadcast channel2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) | 1 Sep 2010
- Effective condition number and its applicationsComputing, Vol. 89, No. 1-2 | 22 June 2010
- Successive projection iterative method for solving matrix equation AX=BJournal of Computational and Applied Mathematics, Vol. 234, No. 8 | 1 Aug 2010
- The structured distance to uncontrollability under multi-perturbations: An approach using multi-valued linear operatorsSystems & Control Letters, Vol. 59, No. 8 | 1 Aug 2010
- Investigations into reconstruction techniques for the National Ignition Facility Neutron Imaging SystemJournal of Physics: Conference Series, Vol. 244, No. 3 | 16 September 2010
- Measurement of jet fragmentation p + p collision at = 200 GeV with the PHENIX detectorJournal of Physics: Conference Series, Vol. 230 | 8 July 2010
- A new and fast implementation for null space based linear discriminant analysisPattern Recognition, Vol. 43, No. 4 | 1 Apr 2010
- Lavoie inequalities for weighted generalized inverses of matricesLinear and Multilinear Algebra, Vol. 58, No. 3 | 1 Apr 2010
- Perturbation Theory Approach to Stellarator Coil OptimizationFusion Science and Technology, Vol. 57, No. 2 | 7 April 2017
- A New and Fast Orthogonal Linear Discriminant Analysis on Undersampled ProblemsSIAM Journal on Scientific Computing, Vol. 32, No. 4 | 4 August 2010
- Other ContributionsG.W. Stewart | 1 Jan 2010
- Relative perturbation bounds for weighted polar decompositionComputers & Mathematics with Applications, Vol. 59, No. 2 | 1 Jan 2010
- Restricted real perturbation values with applications to the structured real controllability radius of LTI systemsProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference | 1 Dec 2009
- The condition numbers for weighted Moore–Penrose inverse and weighted linear least squares problemApplied Mathematics and Computation, Vol. 215, No. 1 | 1 Sep 2009
- A Jacobi–Davidson type method for the generalized singular value problemLinear Algebra and its Applications, Vol. 431, No. 3-4 | 1 Jul 2009
- Compare time series mining approaches for mapping function assessment2009 International Conference on Communications, Circuits and Systems | 1 Jul 2009
- Efficient GSVD Based Multi-User MIMO Linear Precoding and Antenna Selection Scheme2009 IEEE International Conference on Communications | 1 Jun 2009
- Minimax entropy solutions of ill-posed problemsQuarterly of Applied Mathematics, Vol. 67, No. 1 | 8 January 2009
- Error estimation for a weighted minimum-norm least squares solution with positive definite weightsComputational Mathematics and Mathematical Physics, Vol. 49, No. 3 | 6 April 2009
- A Note on Backward Error Analysis of the Generalized Singular Value DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 30, No. 4 | 16 October 2008
- Linear parameter estimation of rational biokinetic functionsWater Research, Vol. 43, No. 1 | 1 Jan 2009
- Generalized real perturbation values with applications to the structured real controllability radius of LTI systems2009 American Control Conference | 1 Jan 2009
- Time Series Mining Approach for Noninvasive Intracranial Pressure Assessment: An Investigation of Different Regularization Techniques2009 WRI World Congress on Computer Science and Information Engineering | 1 Jan 2009
- Combining transcriptional datasets using the generalized singular value decompositionBMC Bioinformatics, Vol. 9, No. 1 | 8 August 2008
- Reliability analysis of computer solutions of systems of linear algebraic equations with approximate initial dataCybernetics and Systems Analysis, Vol. 44, No. 6 | 4 December 2008
- Perturbation bounds for weighted polar decomposition in the weighted unitarily invariant normNumerical Linear Algebra with Applications, Vol. 15, No. 8 | 19 March 2008
- Text categorization via generalized discriminant analysisInformation Processing & Management, Vol. 44, No. 5 | 1 Sep 2008
- Effective condition number for numerical partial differential equationsNumerical Linear Algebra with Applications, Vol. 15, No. 7 | 7 February 2008
- Weighted UDV∗-decomposition and weighted spectral decomposition for rectangular matrices and their applicationsApplied Mathematics and Computation, Vol. 198, No. 1 | 1 Apr 2008
- On level-2 condition number for the weighted Moore–Penrose inverseComputers & Mathematics with Applications, Vol. 55, No. 4 | 1 Feb 2008
- The representation and approximation for the weighted Minkowski inverse in Minkowski spaceMathematical and Computer Modelling, Vol. 47, No. 3-4 | 1 Feb 2008
- Weighted Polar Decomposition and WGL Partial Ordering of Rectangular Complex MatricesSIAM Journal on Matrix Analysis and Applications, Vol. 30, No. 2 | 17 September 2008
- Cluster-Preserving Dimension Reduction Methods for Document ClassificationSurvey of Text Mining II | 1 Jan 2008
- Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. I. Positive definite weightsCybernetics and Systems Analysis, Vol. 44, No. 1 | 1 Jan 2008
- Efficient and spurious-free integral-equation-based optical waveguide mode solverOptics Express, Vol. 15, No. 22 | 18 October 2007
- Discriminant Subspace Analysis: A Fukunaga-Koontz ApproachIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 29, No. 10 | 1 Oct 2007
- KERNEL GBDA FOR RELEVANCE FEEDBACK IN IMAGE RETRIEVALInternational Journal of Image and Graphics, Vol. 07, No. 04 | 20 November 2011
- Vector least-squares solutions for coupled singular matrix equationsJournal of Computational and Applied Mathematics, Vol. 206, No. 2 | 1 Sep 2007
- A Partial Condition Number for Linear Least Squares ProblemsSIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 2 | 3 April 2007
- Using discriminant analysis for multi-class classification: an experimental investigationKnowledge and Information Systems, Vol. 10, No. 4 | 24 March 2006
- Condition numbers with their condition numbers for the weighted moore-penrose inverse and the weighted least squares solutionJournal of Applied Mathematics and Computing, Vol. 22, No. 1-2 | 1 Sep 2006
- Spatial interest pixels (SIPs): useful low-level features of visual media dataMultimedia Tools and Applications, Vol. 30, No. 1 | 1 June 2006
- An improved Newton iteration for the weighted Moore–Penrose inverseApplied Mathematics and Computation, Vol. 174, No. 2 | 1 Mar 2006
- Solving the small sample size problem in face recognition using generalized discriminant analysisPattern Recognition, Vol. 39, No. 2 | 1 Feb 2006
- An Algorithm for High-Dimensional Traffic Data ClusteringFuzzy Systems and Knowledge Discovery | 1 Jan 2006
- Jointly Analyzing Gene Expression and Copy Number Data in Breast Cancer Using Data Reduction ModelsIEEE/ACM Transactions on Computational Biology and Bioinformatics, Vol. 3, No. 1 | 1 Jan 2006
- Matrix Rank Reduction for Data Analysis and Feature ExtractionHandbook of Parallel Computing and Statistics | 30 January 2010
- Linear Algebra, ComputationalEncyclopedia of Statistical Sciences | 15 August 2006
- A two-stage linear discriminant analysis via QR-decompositionIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No. 6 | 1 Jun 2005
- Generalized Regularization Techniques with Constraints for the Analysis of Solar Bremsstrahlung X-ray SpectraSolar Physics, Vol. 225, No. 2 | 1 Dec 2004
- Linear Algebra, ComputationalEncyclopedia of Statistical Sciences | 15 October 2004
- Matrices with special reference to applications in psychometricsLinear Algebra and its Applications, Vol. 388 | 1 Sep 2004
- Some topics on weighted Moore–Penrose inverse, weighted least squares and weighted regularized Tikhonov problemsApplied Mathematics and Computation, Vol. 157, No. 1 | 1 Sep 2004
- Generalized inverse A(2)T,S and a rank equationApplied Mathematics and Computation, Vol. 155, No. 2 | 1 Aug 2004
- An optimization criterion for generalized discriminant analysis on undersampled problemsIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No. 8 | 1 Aug 2004
- Generalizing discriminant analysis using the generalized singular value decompositionIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No. 8 | 1 Aug 2004
- Displacement structure of weighted pseudoinversesApplied Mathematics and Computation, Vol. 153, No. 2 | 1 Jun 2004
- Weighted Tikhonov filter matrices for ill-posed problemsApplied Mathematics and Computation, Vol. 149, No. 2 | 1 Feb 2004
- Cluster-Preserving Dimension Reduction Methods for Efficient Classification of Text DataSurvey of Text Mining | 1 Jan 2004
- Condition numbers and perturbation of the weighted Moore–Penrose inverse and weighted linear least squares problemApplied Mathematics and Computation, Vol. 145, No. 1 | 1 Dec 2003
- A note on the sensitivity of the solution of the weighted linear least squares problemApplied Mathematics and Computation, Vol. 145, No. 2-3 | 1 Dec 2003
- Structure Preserving Dimension Reduction for Clustered Text Data Based on the Generalized Singular Value DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 25, No. 1 | 31 July 2006
- Algorithms for the Inverse Problem of ElectrocardiographyComputational Methods in Biophysics, Biomaterials, Biotechnology and Medical Systems | 1 Jan 2003
- Relationships among Various Kinds of Eigenvalue and Singular Value DecompositionsNew Developments in Psychometrics | 1 Jan 2003
- An implicit Jacobi-like method for computing generalized hyperbolic SVDLinear Algebra and its Applications, Vol. 358, No. 1-3 | 1 Jan 2003
- Inverse problem theory in the optical depth profilometry of thin filmsReview of Scientific Instruments, Vol. 73, No. 12 | 1 Dec 2002
- Evaluating products of matrix pencils and collapsing matrix productsNumerical Linear Algebra with Applications, Vol. 8, No. 6-7 | 31 July 2001
- The weighted Moore–Penrose inverse of modified matricesApplied Mathematics and Computation, Vol. 122, No. 1 | 1 Jul 2001
- The representation and approximation for the weighted Moore–Penrose inverseApplied Mathematics and Computation, Vol. 121, No. 1 | 1 May 2001
- On Accurate Quotient Singular Value Computation in Floating-Point ArithmeticSIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 3 | 31 July 2006
- A regularization approach for the determination of remission curvesInverse Problems in Engineering, Vol. 9, No. 2 | 1 Jan 2001
- Successive matrix squaring algorithm for parallel computing the weighted generalized inverse AMN+Applied Mathematics and Computation, Vol. 116, No. 3 | 1 Dec 2000
- Some new properties of the equality constrained and weighted least squares problemLinear Algebra and its Applications, Vol. 320, No. 1-3 | 1 Nov 2000
- The 2.5 THz heterodyne spectrometer THOMAS: Measurement of OH in the middle atmosphere and comparison with photochemical model resultsJournal of Geophysical Research: Atmospheres, Vol. 105, No. D17 | 1 September 2000
- On a variational formulation of the QSVD and the RSVDLinear Algebra and its Applications, Vol. 311, No. 1-3 | 1 May 2000
- Relative perturbation theory: IV. sin 2θ theoremsLinear Algebra and its Applications, Vol. 311, No. 1-3 | 1 May 2000
- Optimal perturbation bounds for the Hermitian eigenvalue problemLinear Algebra and its Applications, Vol. 309, No. 1-3 | 1 Apr 2000
- Expression for the perturbation of the weighted Moore-Penrose inverseComputers & Mathematics with Applications, Vol. 39, No. 5-6 | 1 Mar 2000
- Two Purposes for Matrix Factorization: A Historical AppraisalSIAM Review, Vol. 42, No. 1 | 4 August 2006
- Updating a Generalized URV DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 2 | 31 July 2006
- New Accurate Algorithms for Singular Value Decomposition of Matrix TripletsSIAM Journal on Matrix Analysis and Applications, Vol. 21, No. 3 | 31 July 2006
- On the Computation of the Restricted Singular Value Decomposition via the Cosine-Sine DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 2 | 31 July 2006
- Condition Number and Backward Error for the Generalized Singular Value DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 2 | 31 July 2006
- Computing approximate stationary distributions for discrete Markov processes with banded infinitesimal generatorsJournal of Applied Probability, Vol. 36, No. 04 | 14 July 2016
- Computing approximate stationary distributions for discrete Markov processes with banded infinitesimal generatorsJournal of Applied Probability, Vol. 36, No. 4 | 14 July 2016
- Perturbation bound of singular linear systemsApplied Mathematics and Computation, Vol. 105, No. 2-3 | 1 Nov 1999
- Methods and algorithms of solving spectral problems for polynomial and rational matricesJournal of Mathematical Sciences, Vol. 96, No. 3 | 1 Sep 1999
- A practical regularization for seismic tomographyGeophysical Journal International, Vol. 138, No. 2 | 1 Aug 1999
- A comparison of higher-order generalized eigensystem techniques and tikhonov regularization for the inverse problem of electrocardiography *Inverse Problems in Engineering, Vol. 7, No. 2 | 1 Apr 1999
- Perturbation Bounds for Least Squares Problems with Equality ConstraintsJournal of Mathematical Analysis and Applications, Vol. 229, No. 2 | 1 Jan 1999
- Parallel Computation of the SVD of a Matrix ProductRecent Advances in Parallel Virtual Machine and Message Passing Interface | 19 April 2002
- Verification Algorithms for Generalized Singular ValuesMathematische Nachrichten, Vol. 208, No. 1 | 20 September 2010
- Construction and Algebraic Characterizations of the Planar and Axial Transportation ProblemsJournal of Mathematical Analysis and Applications, Vol. 220, No. 2 | 1 Apr 1998
- Tikhonov regularization and prior information in electrical impedance tomographyIEEE Transactions on Medical Imaging, Vol. 17, No. 2 | 1 Apr 1998
- Modifying the generalized singular value decomposition with application with application in direction-of-arrival findingBIT Numerical Mathematics, Vol. 38, No. 1 | 1 Mar 1998
- New perturbation results for equality-constrained least squares problemsLinear Algebra and its Applications, Vol. 272, No. 1-3 | 1 Mar 1998
- A Tangent Algorithm for Computing the Generalized Singular Value DecompositionSIAM Journal on Numerical Analysis, Vol. 35, No. 5 | 25 July 2006
- Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on RegularizationSIAM Review, Vol. 40, No. 3 | 2 August 2006
- Relative Perturbation Theory: I. Eigenvalue and Singular Value VariationsSIAM Journal on Matrix Analysis and Applications, Vol. 19, No. 4 | 31 July 2006
- On a Variational Formulation of the Generalized Singular Value DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 18, No. 4 | 31 July 2006
- The SSATS Algorithm and Subspace MethodsApplications of Computer Aided Time Series Modeling | 1 Jan 1997
- Parallel (M−N)SVD algorithms on the SIMD computersWuhan University Journal of Natural Sciences, Vol. 1, No. 3-4 | 1 Dec 1996
- Damage detection by system identification. An application of the generalized singular value decompositionArchive of Applied Mechanics, Vol. 66, No. 8 | 1 Sep 1996
- Computing eigenvalues and singular values of Toeplitz matricesCALCOLO, Vol. 33, No. 3-4 | 1 Sep 1996
- When Does A * A = B * B and Why Does One Want to Know?The American Mathematical Monthly, Vol. 103, No. 6 | 18 April 2018
- Parametric identification of transfer functions in the frequency domain-a surveyIEEE Transactions on Automatic Control, Vol. 39, No. 11 | 1 Nov 1994
- Structures and uniqueness conditions of MK-weighted pseudoinversesBIT, Vol. 34, No. 3 | 1 Sep 1994
- History and generality of the CS decompositionLinear Algebra and its Applications, Vol. 208-209 | 1 Sep 1994
- Multilayer neural networks for reduced-rank approximationIEEE Transactions on Neural Networks, Vol. 5, No. 5 | 1 Sep 1994
- Generalized Epsilon-PseudospectraSIAM Journal on Numerical Analysis, Vol. 31, No. 4 | 14 July 2006
- ESPRIT Direction-of-Arrival Estimation in the Presence of Spatially Correlated NoiseSIAM Journal on Matrix Analysis and Applications, Vol. 15, No. 1 | 31 July 2006
- On the Structure of Generalized Singular Value and QR DecompositionsSIAM Journal on Matrix Analysis and Applications, Vol. 15, No. 1 | 31 July 2006
- Analysis of the generalized total least squares problemAX?B when some columns ofA are free of errorNumerische Mathematik, Vol. 65, No. 1 | 1 Dec 1993
- Computing the Generalized Singular Value DecompositionSIAM Journal on Scientific Computing, Vol. 14, No. 6 | 13 July 2006
- A New Preprocessing Algorithm for the Computation of the Generalized Singular Value DecompositionSIAM Journal on Scientific Computing, Vol. 14, No. 4 | 13 July 2006
- Subspace algorithms for the stochastic identification problemAutomatica, Vol. 29, No. 3 | 1 May 1993
- Bounds on Perturbations of Generalized Singular Values and of Associated SubspacesSIAM Journal on Matrix Analysis and Applications, Vol. 14, No. 1 | 17 July 2006
- Numerical tools for analysis and solution of Fredholm integral equations of the first kindInverse Problems, Vol. 8, No. 6 | 1 January 1999
- Generalizations of the Singular Value and QR-DecompositionsSIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 4 | 17 July 2006
- Perturbation Theory for the Rank-Deficient Equality Constrained Least Squares ProblemSIAM Journal on Numerical Analysis, Vol. 29, No. 5 | 14 July 2006
- On the structure and geometry of the product singular value decompositionLinear Algebra and its Applications, Vol. 168 | 1 Apr 1992
- A reliable and fast method for the solution of Fredhol integral equations of the first kind based on Tikhonov regularizationComputer Physics Communications, Vol. 69, No. 1 | 1 Feb 1992
- Algebraic properties of the rank-deficient equality-constrained and weighted least squares problemsLinear Algebra and its Applications, Vol. 161 | 1 Jan 1992
- Chapter 6 A survey of matrix computationsComputing | 1 Jan 1992
- Generalizations of the singular value and QR decompositionsSignal Processing, Vol. 25, No. 2 | 1 Nov 1991
- An accurate product SVD algorithmSignal Processing, Vol. 25, No. 2 | 1 Nov 1991
- An Algorithm for $Ax = \lambda Bx$ with Symmetric and Positive-Definite A and BSIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 4 | 17 July 2006
- Multivariate, minimum-curvature splines for randomly-spaced dataNavigation and Control Conference | 17 August 1991
- The Restricted Singular Value Decomposition: Properties and ApplicationsSIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 3 | 17 July 2006
- Further results on the spectral decomposition of an incidence matrixJournal of Mathematical Analysis and Applications, Vol. 158, No. 2 | 1 Jul 1991
- The Restricted Total Least Squares Problem: Formulation, Algorithm, and PropertiesSIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 2 | 17 July 2006
- Estimator-correlator array processing: Theoretical underpinnings and adaptive implementationMultidimensional Systems and Signal Processing, Vol. 2, No. 1 | 1 Mar 1991
- A continuous Jacobi-like approach to the simultaneous reduction of real matricesLinear Algebra and its Applications, Vol. 147 | 1 Mar 1991
- A tree of generalizations of the ordinary singular value decompositionLinear Algebra and its Applications, Vol. 147 | 1 Mar 1991
- The Restricted Singular Value Decomposition of Matrix TripletsSIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 1 | 17 July 2006
- SVD-based subspace methods for multivariable continuous-time systems identificationIdentification of Continuous-Time Systems | 1 Jan 1991
- Algebraic characterizations of the singular value decompositions in the transportation problemJournal of Mathematical Analysis and Applications, Vol. 154, No. 1 | 1 Jan 1991
- An unsupervised neural model for oriented principal component extraction[Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing | 1 Jan 1991
- The discrete picard condition for discrete ill-posed problemsBIT, Vol. 30, No. 4 | 1 Dec 1990
- Order-recursive factorization of the pseudoinverse of a covariance matrixIEEE Transactions on Automatic Control, Vol. 35, No. 12 | 1 Dec 1990
- Relations between SVD and GSVD of Discrete regularization problems in standard and general formLinear Algebra and its Applications, Vol. 141 | 1 Nov 1990
- Regularization and the general Gauss-Markov linear modelMathematics of Computation, Vol. 55, No. 192 | 1 January 1990
- Canonical correlations and generalized SVD: applications and new algorithmsParallel Algorithms for Numerical Linear Algebra | 1 Jan 1990
- Least squares methodsHandbook of Numerical Analysis Volume 1 | 1 Jan 1990
- QSVD approach to on- and off-line state-space identificationInternational Journal of Control, Vol. 51, No. 5 | 22 October 2007
- Canonical variate analysis in identification, filtering, and adaptive control29th IEEE Conference on Decision and Control | 1 Jan 1990
- Regularization,GSVD and truncatedGSVDBIT, Vol. 29, No. 3 | 1 Sep 1989
- Canonical correlations and generalized SVD: Applications and new algorithmsJournal of Computational and Applied Mathematics, Vol. 27, No. 1-2 | 1 Sep 1989
- Analysis and Properties of the Generalized Total Least Squares Problem $AX \approx B$ When Some or All Columns in A are Subject to ErrorSIAM Journal on Matrix Analysis and Applications, Vol. 10, No. 3 | 17 July 2006
- Reduced-rank models for interaction in unequally replicated two-way classificationsJournal of Multivariate Analysis, Vol. 28, No. 1 | 1 Jan 1989
- Leverage in Bayesian RegressionBiometrical Journal, Vol. 31, No. 7 | 18 January 2007
- Finite-dimensional regularization with nonidentity smoothing matricesLinear Algebra and its Applications, Vol. 111 | 1 Dec 1988
- Computation of the singular value expansionComputing, Vol. 40, No. 3 | 1 Sep 1988
- Numerical treatment of restricted gauss-markov model 1Communications in Statistics - Simulation and Computation, Vol. 17, No. 2 | 1 Jan 1988
- Interlacing inequalities for generalized singular valuesLinear Algebra and its Applications, Vol. 87 | 1 Mar 1987
- Computing the Generalized Singular Value DecompositionSIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 4 | 14 July 2006
- RGSVD—AN Algorithm for Computing the Kronecker Structure and Reducing Subspaces of Singular $A - \lambda B$ PencilsSIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 1 | 14 July 2006
- Computing the CS and the generalized singular value decompositionsNumerische Mathematik, Vol. 46, No. 4 | 1 Dec 1985
- A mathematical procedure for solving the inverse potential problem of electrocardiography. analysis of the time-space accuracy from in vitro experimental dataMathematical Biosciences, Vol. 77, No. 1-2 | 1 Dec 1985
- On the Method of Weighting for Equality-Constrained Least-Squares ProblemsSIAM Journal on Numerical Analysis, Vol. 22, No. 5 | 14 July 2006
- The general linear model and the generalized singular value decompositionLinear Algebra and its Applications, Vol. 70 | 1 Oct 1985
- The singular value decomposition in multivariate statisticsACM SIGNUM Newsletter, Vol. 20, No. 3 | 1 July 1985
- ‘Fat’ triangulations, or solving certain nonconvex matrix optimization problemsMathematical Programming, Vol. 31, No. 2 | 1 Jun 1985
- The generalized singular value decomposition and the general (A-λB)-problemBIT, Vol. 24, No. 4 | 1 Dec 1984
- The perturbation bounds for eigenspaces of a definite matrix-pairNumerische Mathematik, Vol. 41, No. 3 | 1 Oct 1983
- Isolating Error Effects in Solving Ill-Posed ProblemsSIAM Journal on Algebraic Discrete Methods, Vol. 4, No. 3 | 17 July 2006
- Perturbation Analysis for the Generalized Singular Value ProblemSIAM Journal on Numerical Analysis, Vol. 20, No. 3 | 17 July 2006
- Pitfalls in the Numerical Solution of Linear Ill-Posed ProblemsSIAM Journal on Scientific and Statistical Computing, Vol. 4, No. 2 | 14 July 2006
- Some Inverse Problems in ElectrocardiologyNumerical Treatment of Inverse Problems in Differential and Integral Equations | 1 Jan 1983
- A method for computing the generalized singular value decompositionMatrix Pencils | 24 August 2006
- Perturbation analysis for the generalized eigenvalue and the generalized singular value problemMatrix Pencils | 24 August 2006
- A generalized SVD analysis of some weighting methods for equality constrained least squaresMatrix Pencils | 24 August 2006
- A weighted pseudoinverse, generalized singular values, and constrained least squares problemsBIT, Vol. 22, No. 4 | 1 Dec 1982
- Computing theCS decomposition of a partitioned orthonormal matrixNumerische Mathematik, Vol. 40, No. 3 | 1 Oct 1982
- Towards a Generalized Singular Value DecompositionSIAM Journal on Numerical Analysis, Vol. 18, No. 3 | 17 July 2006
- Least squares with a quadratic constraintNumerische Mathematik, Vol. 36, No. 3 | 1 Sep 1980
- Perturbation Theory for the Least Squares Problem with Linear Equality ConstraintsSIAM Journal on Numerical Analysis, Vol. 17, No. 3 | 17 July 2006
- A Practical Examination of Some Numerical Methods for Linear Discrete Ill-Posed ProblemsSIAM Review, Vol. 21, No. 1 | 10 July 2006
- Algorithms for the regularization of ill-conditioned least squares problemsBIT, Vol. 17, No. 2 | 1 Jun 1977
- The impact of the singular value decomposition in system theory, signal processing, and circuit theoryThree Decades of Mathematical System Theory
- Automated and optimal system identification by canonical variablesProceedings of 1994 American Control Conference - ACC '94
- Automated and Objective System Identification Based on Canonical VariablesProceedings. The First IEEE Regional Conference on Aerospace Control Systems,
- Order-recursive factorization of the pseudoinverse of a covariance matrixProceedings of the 27th IEEE Conference on Decision and Control
- Generalized canonical variate analysis of nonlinear systemsProceedings of the 27th IEEE Conference on Decision and Control
- Subspace algorithms for the stochastic identification problem[1991] Proceedings of the 30th IEEE Conference on Decision and Control
- Parametric identification of transfer functions in the frequency domain: a surveyProceedings of 32nd IEEE Conference on Decision and Control
- The quotient SVD and directional aspects of 2 transfer matricesCompEuro 1992 Proceedings Computer Systems and Software Engineering
- Computing the singular values of the product of two matrices in distributed memory multiprocessorsProceedings of 4th Euromicro Workshop on Parallel and Distributed Processing
- Spatial interest pixels (SIPs): useful low-level features of visual media dataThird IEEE International Conference on Data Mining
- A new optimization criterion for generalized discriminant analysis on undersampled problemsThird IEEE International Conference on Data Mining
- Space-time treatment of inverse bioelectric field problemsProceedings of the 22nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (Cat. No.00CH37143)
- Linear space-time transmitter and receiver processing and scheduling for the MIMO broadcast channel2004 IEEE 59th Vehicular Technology Conference. VTC 2004-Spring (IEEE Cat. No.04CH37514)