Towards a Generalized Singular Value Decomposition
Abstract
We suggest a form for, and give a constructive derivation of, the generalized singular value decomposition of any two matrices having the same number of columns. We outline its desirable characteristics and compare it to an earlier suggestion by Van Loan [SIAM J. Numer. Anal., 13 (1976), pp. 76–83]. The present form largely follows from the work of Van Loan, but is slightly more general and computationally more amenable than that in the paper cited. We also prove a useful extension of a theorem of Stewart [SIAM Rev. 19 (1977), pp. 634–662] on unitary decompositions of submatrices of a unitary matrix.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chandler Davis, W. M. Kahan, The rotation of eigenvectors by a perturbation. III, SIAM J. Numer. Anal., 7 (1970), 1–46
2.
J. J. Dongarra, C. B. Moler, J. R. Bunch, G. W. Stewart, LINPACK Users' Guide, Society for Industrial and Applied Mathematics, Philadelphia, 1979
3.
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
4.
G. H. Golub, C. Reinsch, Singular value decomposition and least squares solutions, Numer. Math., 14 (1970), 403–420
5.
Alston S. Householder, Unitary triangularization of a nonsymmetric matrix, J. Assoc. Comput. Mach., 5 (1958), 339–342
6.
Charles Lawson, Richard Hanson, Solving least squares problems, Prentice-Hall Inc., Englewood Cliffs, N.J., 1974xii+340
7.
G. W. Stewart, On the perturbation of pseudo-inverses, projections and linear least squares problems, SIAM Rev., 19 (1977), 634–662
8.
Charles F. Van Loan, A general matrix eigenvalue algorithm, SIAM J. Numer. Anal., 12 (1975), 819–834
9.
Charles F. Van Loan, Generalizing the singular value decomposition, SIAM J. Numer. Anal., 13 (1976), 76–83
10.
Charles F. Van Loan, On Stewart's singular value decomposition for partitioned orthogonal matrices, Stanford University Rep., CS79-767, Stanford University, Stanford, CA., 1979
11.
J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965xviii+662
Information & Authors
Information
Published In
Copyright
Copyright © 1981 Society for Industrial and Applied Mathematics.
History
Submitted: 30 January 1980
Published online: 17 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
- Generalized Matrix Nearness ProblemsSIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 4 | 10 November 2023
- The impact of horizontal resolution on the representation of atmospheric circulation types in Western Europe using the MPI‐ESM modelInternational Journal of Climatology, Vol. 43, No. 14 | 9 August 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
- A Generic Approach on Current Technologies in Metaverse2023 4th International Conference on Smart Electronics and Communication (ICOSEC) | 20 Sep 2023
- Thick-restarted joint Lanczos bidiagonalization for the GSVDJournal of Computational and Applied Mathematics, Vol. 13 | 1 Aug 2023
- Fifty Three Matrix Factorizations: A Systematic ApproachSIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 2 | 25 April 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
- Compressive sensing-based tomography for Absolute X-ray UltraViolet (AXUV) diagnosticsReview of Scientific Instruments, Vol. 94, No. 6 | 14 June 2023
- Signal Processing for Highly Resolved 2D NMRFast 2D Solution-state NMR | 17 May 2023
- Summary of Static Graph Embedding Algorithms2023 4th International Conference on Computer Vision, Image and Deep Learning (CVIDL) | 12 May 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
- 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
- Domain Adaptation Principal Component Analysis: Base Linear Method for Learning with Out-of-Distribution DataEntropy, Vol. 25, No. 1 | 24 December 2022
- Learning spectral windowing parameters for regularization using unbiased predictive risk and generalized cross validation techniques for multiple data setsInverse Problems and Imaging, Vol. 0, No. 0 | 1 Jan 2023
- How to Enrich Metaverse? Blockchains, AI, and Digital TwinFrom Blockchain to Web3 & Metaverse | 25 May 2023
- Linear AlgebraScalable Algorithms for Contact Problems | 4 May 2023
- A direct method for updating mass and stiffness matrices with submatrix constraintsLinear and Multilinear Algebra, Vol. 70, No. 19 | 22 January 2021
- The Re-nnd and Re-pd solutions to the matrix equations AX = C , XB = DLinear and Multilinear Algebra, Vol. 70, No. 18 | 11 November 2020
- 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
- Improving MIMO Secrecy Rate through Efficient Power Allocation2022 IEEE 96th Vehicular Technology Conference (VTC2022-Fall) | 1 Sep 2022
- Learning Traffic Network Embeddings for Predicting Congestion PropagationIEEE Transactions on Intelligent Transportation Systems, Vol. 23, No. 8 | 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
- A Survey of Unsupervised Generative Models for Exploratory Data Analysis and Representation LearningACM Computing Surveys, Vol. 54, No. 5 | 9 July 2021
- On the Cartan decomposition for classical random matrix ensemblesJournal of Mathematical Physics, Vol. 63, No. 6 | 15 June 2022
- ReferencesMultiblock Data Fusion in Statistics and Machine Learning | 15 April 2022
- Master stability functions for metacommunities with two types of habitatsPhysical Review E, Vol. 105, No. 4 | 15 April 2022
- An alternative approach for solving the quadratic matrix equation C∗X∗AXC+C∗X∗B+B∗XC+D=0Journal of Computational and Applied Mathematics, Vol. 404 | 1 Apr 2022
- A Generalized CUR Decomposition for Matrix PairsSIAM Journal on Mathematics of Data Science, Vol. 4, No. 1 | 17 March 2022
- Tensorial conditional gradient method for solving multidimensional ill-posed problemsApplied Numerical Mathematics, Vol. 173 | 1 Mar 2022
- Directed Network Embedding with Virtual Negative EdgesProceedings of the Fifteenth ACM International Conference on Web Search and Data Mining | 15 February 2022
- Fusing Blockchain and AI With Metaverse: A SurveyIEEE Open Journal of the Computer Society, Vol. 3 | 1 Jan 2022
- A Multistage Framework With Mean Subspace Computation and Recursive Feedback for Online Unsupervised Domain AdaptationIEEE Transactions on Image Processing, Vol. 31 | 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
- An Experimental Survey of Missing Data Imputation AlgorithmsIEEE Transactions on Knowledge and Data Engineering, Vol. 25 | 1 Jan 2022
- Free Energy Node Embedding via Generalized Skip-gram with Negative SamplingIEEE Transactions on Knowledge and Data Engineering, Vol. 33 | 1 Jan 2022
- Theoretical and experimental determination of proppant‐crushing ratio and fracture conductivity with different particle sizesEnergy Science & Engineering, Vol. 10, No. 1 | 19 November 2021
- Learning Latent Variable Models with Regularization2021 International Conference on Electrical, Computer and Energy Technologies (ICECET) | 9 Dec 2021
- Edge Intelligence: Empowering Intelligence to the Edge of NetworkProceedings of the IEEE, Vol. 109, No. 11 | 1 Nov 2021
- The joint bidiagonalization process with partial reorthogonalizationNumerical Algorithms, Vol. 88, No. 2 | 26 January 2021
- Roundoff Error Analysis of an Algorithm Based on Householder Bidiagonalization for Total Least Squares ProblemsMathematics, Vol. 9, No. 20 | 12 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
- Randomized algorithms for generalized singular value decomposition with application to sensitivity analysisNumerical Linear Algebra with Applications, Vol. 28, No. 4 | 24 February 2021
- Digital Watermark Perturbation for Adversarial Examples to Fool Deep Neural Networks2021 International Joint Conference on Neural Networks (IJCNN) | 18 Jul 2021
- Neural network for computing GSVD and RSVDNeurocomputing, Vol. 444 | 1 Jul 2021
- NeoCyberKG: Enhancing Cybersecurity Laboratories with a Machine Learning-enabled Knowledge GraphProceedings of the 26th ACM Conference on Innovation and Technology in Computer Science Education V. 1 | 26 June 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
- Linear Algebra, ComputationalWiley StatsRef: Statistics Reference Online | 17 May 2021
- Linear Discriminant Analysis-Based Motion Classification Using Distributed Micro-Doppler Radars with Limited BackhaulSensors, Vol. 21, No. 9 | 21 April 2021
- On worst-case condition numbers of a multiple nonzero finite generalized singular valueLinear Algebra and its Applications, Vol. 616 | 1 May 2021
- Visual Positioning in Indoor Environments Using RGB-D Images and Improved Vector of Local Aggregated DescriptorsISPRS International Journal of Geo-Information, Vol. 10, No. 4 | 24 March 2021
- Condition numbers for the K -weighted pseudoinverse and their statistical estimationLinear and Multilinear Algebra, Vol. 69, No. 4 | 20 May 2019
- Using partial spectral information for block diagonal preconditioning of saddle-point systemsComputational Optimization and Applications, Vol. 78, No. 2 | 4 January 2021
- Randomized Generalized Singular Value DecompositionCommunications on Applied Mathematics and Computation, Vol. 3, No. 1 | 7 March 2020
- Achieving Positive Covert Capacity Over MIMO AWGN ChannelsIEEE Journal on Selected Areas in Information Theory, Vol. 2, No. 1 | 1 Mar 2021
- 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
- Covariance NMR: Theoretical concerns, practical considerations, contemporary applications and related techniquesProgress in Nuclear Magnetic Resonance Spectroscopy, Vol. 122 | 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
- Divide et impera : How disentangling common and distinctive variability in multiset data analysis can aid industrial process troubleshooting and understandingJournal of Chemometrics, Vol. 35, No. 2 | 28 June 2020
- An inverse eigenvalue problem for Hamiltonian matricesJournal of Computational and Applied Mathematics, Vol. 381 | 1 Jan 2021
- Covert MIMO Communications Under Variational Distance ConstraintIEEE Transactions on Information Forensics and Security, Vol. 16 | 1 Jan 2021
- Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO ChannelsIEEE Transactions on Signal Processing, Vol. 69 | 1 Jan 2021
- The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations $ A_1XA_1^\ast = C_1 $ and $ A_2XA_2^\ast = C_2 $AIMS Mathematics, Vol. 7, No. 1 | 1 Jan 2021
- Multi-Array Electron Beam Stabilization using Block-Circulant Transformation and Generalized Singular Value Decomposition2020 59th IEEE Conference on Decision and Control (CDC) | 14 Dec 2020
- Point data reconstruction and smoothing using cubic splines and clusterizationMathematics and Computers in Simulation, Vol. 176 | 1 Oct 2020
- An extension of analytic solutions of a class of constrained matrix minimization problemsJournal of Computational and Applied Mathematics, Vol. 372 | 1 Jul 2020
- Iterative Solution of Weighted Linear Least Squares ProblemsAnalele Universitatii "Ovidius" Constanta - Seria Matematica, Vol. 28, No. 2 | 22 September 2020
- Positive semidefinite programming: mixed, parallel, and width-independentProceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing | 6 June 2020
- Link prediction based on network embedding and similarity transferring methodsModern Physics Letters B, Vol. 34, No. 16 | 15 May 2020
- Covert MIMO Communications under Variational Distance Constraint2020 IEEE International Symposium on Information Theory (ISIT) | 1 Jun 2020
- Analytic solutions of a class of extended constrained matrix maximization problemsApplied Mathematics and Computation, Vol. 372 | 1 May 2020
- Node proximity preserved dynamic network embedding via matrix perturbationKnowledge-Based Systems, Vol. 196 | 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
- Discriminative Streaming Network EmbeddingKnowledge-Based Systems, Vol. 190 | 1 Feb 2020
- The GSVD: Where are the Ellipses?, Matrix Trigonometry, and MoreSIAM Journal on Matrix Analysis and Applications, Vol. 41, No. 4 | 24 November 2020
- Source Separation With Side Information Based on Gaussian Mixture Models With Application in Art InvestigationIEEE Transactions on Signal Processing, Vol. 68 | 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
- Least squares solutions to the rank-constrained matrix approximation problem in the Frobenius normCalcolo, Vol. 56, No. 4 | 23 October 2019
- Robust Power Allocation in MIMO-NOMA SystemsIEEE Wireless Communications Letters, Vol. 8, No. 6 | 1 Dec 2019
- Submatrix constrained least-squares inverse problem for symmetric matrices from the design of vibrating structuresJournal of Computational and Applied Mathematics, Vol. 355 | 1 Aug 2019
- An Inductive Content-Augmented Network Embedding Model for Edge Artificial IntelligenceIEEE Transactions on Industrial Informatics, Vol. 15, No. 7 | 1 Jul 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
- A Survey on Network EmbeddingIEEE Transactions on Knowledge and Data Engineering, Vol. 31, No. 5 | 1 May 2019
- Brain Connectivity-Informed Regularization Methods for RegressionStatistics in Biosciences, Vol. 11, No. 1 | 6 December 2017
- A simultaneous decomposition for seven matrices with applicationsJournal of Computational and Applied Mathematics, Vol. 349 | 1 Mar 2019
- Enhancing Attributed Network Embedding via Similarity MeasureIEEE Access, Vol. 7 | 1 Jan 2019
- Capturing Edge Attributes via Network EmbeddingIEEE Transactions on Computational Social Systems, Vol. 5, No. 4 | 1 Dec 2018
- Mathematically universal and biologically consistent astrocytoma genotype encodes for transformation and predicts survival phenotypeAPL Bioengineering, Vol. 2, No. 3 | 19 September 2018
- Embedding Networks with Edge AttributesProceedings of the 29th on Hypertext and Social Media | 3 July 2018
- Analytical best approximate Hermitian and generalized skew-Hamiltonian solution of matrix equation AXAH+CYCH=FComputers & Mathematics with Applications, Vol. 75, No. 10 | 1 May 2018
- Compressive Sensing With Side Information: How to Optimally Capture This Extra Information for GMM Signals?IEEE Transactions on Signal Processing, Vol. 66, No. 9 | 1 May 2018
- Lower-mantle plume beneath the Yellowstone hotspot revealed by core wavesNature Geoscience, Vol. 11, No. 4 | 19 March 2018
- Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decompositionGeophysical Journal International, Vol. 213, No. 1 | 17 January 2018
- Linear Precoder Design for an MIMO Gaussian Wiretap Channel With Full-Duplex Source and Destination NodesIEEE Transactions on Information Forensics and Security, Vol. 13, No. 2 | 1 Feb 2018
- The MIMO Wiretap Channel DecomposedIEEE Transactions on Information Theory, Vol. 64, No. 2 | 1 Feb 2018
- 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
- Refining the Lower Bound on the Positive Eigenvalues of Saddle Point Matrices with Insights on the Interactions between the BlocksSIAM Journal on Matrix Analysis and Applications, Vol. 39, No. 2 | 26 April 2018
- High-order Proximity Preserved Embedding For Dynamic NetworksIEEE Transactions on Knowledge and Data Engineering, Vol. 9 | 1 Jan 2018
- Partial condition number for the equality constrained linear least squares problemCalcolo, Vol. 54, No. 4 | 7 April 2017
- Accuracy of singular vectors obtained by projection-based SVD methodsBIT Numerical Mathematics, Vol. 57, No. 4 | 19 June 2017
- A Generalized Singular Value Decomposition Strategy for Estimating the Block Recursive Simultaneous Equations ModelComputational Economics, Vol. 50, No. 3 | 9 June 2016
- Blind separation of partially overlapping data packetsDigital Signal Processing, Vol. 68 | 1 Sep 2017
- Common and distinct components in data fusionJournal of Chemometrics, Vol. 31, No. 7 | 31 May 2017
- MIMO Wiretap ChannelsInformation Theoretic Security and Privacy of Information Systems | 16 Jun 2017
- Simultaneous decomposition of quaternion matrices involving η-Hermicity with applicationsApplied Mathematics and Computation, Vol. 298 | 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
- Hybrid and Iteratively Reweighted Regularization by Unbiased Predictive Risk and Weighted GCV for Projected SystemsSIAM Journal on Scientific Computing, Vol. 39, No. 2 | 9 March 2017
- Goal-Oriented Optimal Approximations of Bayesian Linear Inverse ProblemsSIAM Journal on Scientific Computing, Vol. 39, No. 5 | 26 October 2017
- Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard ParameterSIAM Journal on Scientific Computing, Vol. 39, No. 6 | 28 November 2017
- Sequential Loop Closure Based Adaptive Output FeedbackIEEE Access, Vol. 5 | 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
- Improving Wireless Physical Layer Security via Exploiting Co-Channel InterferenceIEEE Journal of Selected Topics in Signal Processing, Vol. 10, No. 8 | 1 Dec 2016
- Classification and Reconstruction of High-Dimensional Signals From Low-Dimensional Features in the Presence of Side InformationIEEE Transactions on Information Theory, Vol. 62, No. 11 | 1 Nov 2016
- Asymmetric Transitivity Preserving Graph EmbeddingProceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining | 13 August 2016
- Hybrid secure beamforming and vehicle selection using hierarchical agglomerative clustering for C-RAN-based vehicle-to-infrastructure communications in vehicular cyber-physical systemsInternational Journal of Distributed Sensor Networks, Vol. 12, No. 8 | 24 August 2016
- On the design of linear projections for compressive sensing with side information2016 IEEE International Symposium on Information Theory (ISIT) | 1 Jul 2016
- 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
- Inverse problems for (R,S) -symmetric matrices in structural dynamic model updatingComputers & Mathematics with Applications, Vol. 71, No. 5 | 1 Mar 2016
- Submatrix Constrained Inverse Eigenvalue Problem involving Generalised Centrohermitian Matrices in Vibrating Structural Model CorrectionEast Asian Journal on Applied Mathematics, Vol. 6, No. 1 | 27 January 2016
- A Canonical CS Representation of a Pair of SubspacesSIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 2 | 19 April 2016
- Tikhonov Regularization and Randomized GSVDSIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 2 | 19 May 2016
- Rank Decisions in Matrix Quotient DecompositionsSIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 4 | 14 December 2016
- The number of connected components in a graph associated with a rectangular (0,1) -matrixLinear Algebra and its Applications, Vol. 487 | 1 Dec 2015
- On Secrecy Capacity of the Helper-Assisted Gaussian Wiretap Channel with Multi-Antennas2015 IEEE Global Communications Conference (GLOBECOM) | 1 Dec 2015
- AF-Based CSI Feedback for User Selection in Multi-User MIMO Systems2015 IEEE Global Communications Conference (GLOBECOM) | 1 Dec 2015
- Parameter Identification by Iterative Constrained RegularizationJournal of Physics: Conference Series, Vol. 657 | 16 November 2015
- Solving the mixed Sylvester matrix equations by matrix decompositionsComptes Rendus Mathematique, Vol. 353, No. 11 | 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
- Covariance shaping for interference coordination in cellular wireless communication systems2015 49th Asilomar Conference on Signals, Systems and Computers | 1 Nov 2015
- Quantum XOR GamesACM Transactions on Computation Theory, Vol. 7, No. 4 | 31 August 2015
- Phillips-Tikhonov regularization with a priori information for neutron emission tomographic reconstruction on Joint European TorusReview of Scientific Instruments, Vol. 86, No. 9 | 1 Sep 2015
- Low Cost Pre-Coder Design for MIMO AF Two-Way Relay ChannelIEEE Signal Processing Letters, Vol. 22, No. 9 | 1 Sep 2015
- Finite-Element Structural Updating Using Frequency Response FunctionsJournal of Aircraft, Vol. 52, No. 5 | 1 Sep 2015
- Comparing 1D and 2.5D AEM inversions in 3D geological mapping using a new adaptive inversion solver14th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 3-6 August 2015 | 6 August 2015
- Uncorrelated transferable feature extraction for signal classification in brain-computer interfaces2015 International Joint Conference on Neural Networks (IJCNN) | 1 Jul 2015
- Is uncorrelated linear discriminant analysis really a new method?Chemometrics and Intelligent Laboratory Systems, Vol. 142 | 1 Mar 2015
- Identification of the Smart Spring properties from FRFs measurements56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference | 2 January 2015
- Preconditioning Linear Least-Squares Problems by Identifying a Basis MatrixSIAM Journal on Scientific Computing, Vol. 37, No. 5 | 29 October 2015
- Optimal Low-rank Approximations of Bayesian Linear Inverse ProblemsSIAM Journal on Scientific Computing, Vol. 37, No. 6 | 3 November 2015
- Application of the χ2 principle and unbiased predictive risk estimator for determining the regularization parameter in 3-D focusing gravity inversionGeophysical Journal International, Vol. 200, No. 1 | 14 November 2014
- Joint Secure Beamforming and User Selection for Multi-user MISO Systems with Confidential MessagesWireless Algorithms, Systems, and Applications | 1 August 2015
- Matrix Eigenvalue ProblemsNumerical Methods in Matrix Computations | 7 October 2014
- Regularized solution of a nonlinear problem in electromagnetic soundingInverse Problems, Vol. 30, No. 12 | 2 December 2014
- On Secrecy Capacity of the Helper-Assisted Gaussian Wiretap Channel with Multi-Antennas2015 IEEE Global Communications Conference (GLOBECOM) | 1 Dec 2014
- AF-Based CSI Feedback for User Selection in Multi-User MIMO Systems2015 IEEE Global Communications Conference (GLOBECOM) | 1 Dec 2014
- Verified bounds for all the singular values of matrixJapan Journal of Industrial and Applied Mathematics, Vol. 31, No. 3 | 17 May 2014
- Regularization parameter estimation for underdetermined problems by the χ2 principle with application to 2D focusing gravity inversionInverse Problems, Vol. 30, No. 8 | 17 July 2014
- Automatic estimation of the regularization parameter in 2D focusing gravity inversion: application of the method to the Safo manganese mine in the northwest of IranJournal of Geophysics and Engineering, Vol. 11, No. 4 | 22 July 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
- Power allocation in MIMO wiretap channel with statistical CSI and finite-alphabet input2014 International Conference on Signal Processing and Communications (SPCOM) | 1 Jul 2014
- Optimal partial decode-and-forward rates for the Gaussian MIMO relay channel using the GSVD2014 IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) | 1 Jun 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
- Integrative omics analysis. A study based on Plasmodium falciparum mRNA and protein dataBMC Systems Biology, Vol. 8, No. S2 | 13 March 2014
- Finite Element Structural Updating using FRFs55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference | 10 January 2014
- Multi-tissue Analysis of Co-expression Networks by Higher-Order Generalized Singular Value Decomposition Identifies Functionally Coherent Transcriptional ModulesPLoS Genetics, Vol. 10, No. 1 | 2 January 2014
- MIMO Broadcast Channel with an Unknown Eavesdropper: Secrecy Degrees of FreedomIEEE Transactions on Communications, Vol. 62, No. 1 | 1 Jan 2014
- The Solutions to Matrix Equation AX=B with Some ConstraintsJournal of Applied Mathematics, Vol. 2014 | 1 Jan 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
- Identifying common and distinctive processes underlying multiset dataChemometrics and Intelligent Laboratory Systems, Vol. 129 | 1 Nov 2013
- Separation method for multi-source blended seismic dataApplied Geophysics, Vol. 10, No. 3 | 27 December 2013
- MIMO Multiple Access Channel With an Arbitrarily Varying Eavesdropper: Secrecy Degrees of FreedomIEEE Transactions on Information Theory, Vol. 59, No. 8 | 1 Aug 2013
- Joint Wireless Information and Energy Transfer in a Two-User MIMO Interference ChannelIEEE Transactions on Wireless Communications, Vol. 12, No. 8 | 1 Aug 2013
- SLNR-Based Transmit Beamforming for MIMO Wiretap ChannelWireless Personal Communications, Vol. 71, No. 1 | 8 August 2012
- 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
- MMSE-Based Precoder Design in Nonregenerative Relay Systems with Direct Link2013 IEEE 77th Vehicular Technology Conference (VTC Spring) | 1 Jun 2013
- Common and Cluster-Specific Simultaneous Component AnalysisPLoS ONE, Vol. 8, No. 5 | 8 May 2013
- Application of kernel-genetic algorithm as nonlinear feature selection in tropical wood species recognition systemComputers and Electronics in Agriculture, Vol. 93 | 1 Apr 2013
- A note on simple nonzero finite generalized singular valuesLinear Algebra and its Applications, Vol. 438, No. 8 | 1 Apr 2013
- The Jacobi MIMO ChannelIEEE Transactions on Information Theory, Vol. 59, No. 4 | 1 Apr 2013
- Divide and Conquer the CS DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 2 | 25 April 2013
- Least-Squares Transformations between Point-SetsImage Analysis | 1 Jan 2013
- On the Low-Rank Approximation Arising in the Generalized Karhunen-Loeve TransformAbstract and Applied Analysis, Vol. 2013 | 1 Jan 2013
- Eigenvector-Free Solutions to the Matrix Equation AXBH=E with Two Special ConstraintsJournal of Applied Mathematics, 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
- On Secrecy Rate Analysis of MIMO Wiretap Channels Driven by Finite-Alphabet InputIEEE Transactions on Communications, Vol. 60, No. 12 | 1 Dec 2012
- Joint SVD-GSVD precoding technique and secrecy capacity lower bound for the MIMO relay wire-tap channelEURASIP Journal on Wireless Communications and Networking, Vol. 2012, No. 1 | 10 December 2012
- An Outer Bound for the Gaussian MIMO Broadcast Channel With Common and Private MessagesIEEE Transactions on Information Theory, Vol. 58, No. 11 | 1 Nov 2012
- A Closed-Form Power Allocation and Signal Alignment for a Diagonalized MIMO Two-Way Relay Channel With Linear ReceiversIEEE Transactions on Signal Processing, Vol. 60, No. 11 | 1 Nov 2012
- Optimal Approximate Solution of a Class of Matrix EquationApplied Mechanics and Materials, Vol. 220-223 | 1 November 2012
- From NLDA to LDA/GSVD: a modified NLDA algorithmNeural Computing and Applications, Vol. 21, No. 7 | 19 August 2011
- Efficient Lattice-Reduction-Aided Successive Interference Cancellation for Clustered Multiuser MIMO SystemIEEE Transactions on Vehicular Technology, Vol. 61, No. 8 | 1 Oct 2012
- Novel Fisher discriminant classifiersPattern Recognition, Vol. 45, No. 10 | 1 Oct 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
- Fusion of Magnetometer and Gradiometer Sensors of MEG in the Presence of Multiplicative ErrorIEEE Transactions on Biomedical Engineering, Vol. 59, No. 7 | 1 Jul 2012
- DISCO-SCA and Properly Applied GSVD as Swinging Methods to Find Common and Distinctive ProcessesPLoS ONE, Vol. 7, No. 5 | 31 May 2012
- Joint SVD-GSVD Precoding Technique and Secrecy Capacity Lower Bound for the MIMO Relay Wire-Tap Channel2012 IEEE 75th Vehicular Technology Conference (VTC Spring) | 1 May 2012
- Stable Computation of the CS Decomposition: Simultaneous BidiagonalizationSIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 1 | 5 January 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
- Structured penalties for functional linear models—partially empirical eigenvectors for regressionElectronic Journal of Statistics, Vol. 6, No. none | 1 Jan 2012
- An efficient algorithm for clustered integer least squares problemsNumerical Linear Algebra with Applications, Vol. 19, No. 1 | 1 February 2011
- 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 generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = EMathematical Methods in the Applied Sciences, Vol. 34, No. 13 | 16 May 2011
- MIMO multiple access channel with an arbitrarily varying eavesdropper2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton) | 1 Sep 2011
- An image fusion method based on quotient singular value decomposition2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS) | 1 Aug 2011
- Weighted sum rate maximization for the MIMO X channel through MMSE precoding2011 IEEE International Symposium on Information Theory Proceedings | 1 Jul 2011
- Improved Interference Alignment Precoding for the MIMO X Channel2011 IEEE International Conference on Communications (ICC) | 1 Jun 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
- Max-Min Problems on the Ranks and Inertias of the Matrix Expressions A−BXC±(BXC)∗ with ApplicationsJournal of Optimization Theory and Applications, Vol. 148, No. 3 | 23 November 2010
- Diversity-Multiplexing Tradeoff for the Multiple-Antenna Wire-tap ChannelIEEE Transactions on Wireless Communications, Vol. 10, No. 3 | 1 Mar 2011
- Eigenvector-free solutions to AX=B with PX=XP and XH=sX constraintsApplied Mathematics and Computation, Vol. 217, No. 12 | 1 Feb 2011
- A simultaneous decomposition of a matrix triplet with applicationsNumerical Linear Algebra with Applications, Vol. 18, No. 1 | 4 February 2010
- Volume Removed - Publisher's DisclaimerEnergy Procedia, Vol. 13 | 1 Jan 2011
- Real controllability radius of higher-order, descriptor, and time-delay LTI systemsIFAC Proceedings Volumes, Vol. 44, No. 1 | 1 Jan 2011
- On Symmetric and Skew-Symmetric Solutions to a Procrustes ProblemNumerical Linear Algebra in Signals, Systems and Control | 22 May 2011
- Degrees of Freedom Region of the Gaussian MIMO Broadcast Channel with Common and Private Messages2010 IEEE Global Telecommunications Conference GLOBECOM 2010 | 1 Dec 2010
- 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
- Dealing with structural constraints in self-optimizing control engineeringJournal of Process Control, Vol. 20, No. 9 | 1 Oct 2010
- Secure broadcasting using multiple antennasJournal of Communications and Networks, Vol. 12, No. 5 | 1 Oct 2010
- A modified NLDA algorithm2010 IEEE International Conference on Image Processing | 1 Sep 2010
- NPDA/CS: Improved Non-parametric Discriminant Analysis with CS decomposition and its application to face recognition2010 IEEE International Conference on Image Processing | 1 Sep 2010
- Least-squares solutions to the matrix equations AX=B and XC=DApplied Mathematics and Computation, Vol. 216, No. 10 | 1 Jul 2010
- A new and fast implementation for null space based linear discriminant analysisPattern Recognition, Vol. 43, No. 4 | 1 Apr 2010
- 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
- The least squares problem of the matrix equation A 1 X 1 B 1 T + A 2 X 2 B 2 T = TApplied Mathematics-A Journal of Chinese Universities, Vol. 24, No. 4 | 8 December 2009
- 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
- Implementation of incremental linear discriminant analysis using singular value decomposition for face recognition2009 First International Conference on Advanced Computing | 1 Dec 2009
- Correlating gene and protein expression data using Correlated Factor AnalysisBMC Bioinformatics, Vol. 10, No. 1 | 1 September 2009
- COMPREHENSIVE ANALYSIS FOR THE LOCAL FISHER DISCRIMINANT ANALYSISInternational Journal of Pattern Recognition and Artificial Intelligence, Vol. 23, No. 06 | 21 November 2011
- A Jacobi–Davidson type method for the generalized singular value problemLinear Algebra and its Applications, Vol. 431, No. 3-4 | 1 Jul 2009
- Efficient GSVD Based Multi-User MIMO Linear Precoding and Antenna Selection Scheme2009 IEEE International Conference on Communications | 1 Jun 2009
- Error estimates for the regularization of least squares problemsNumerical Algorithms, Vol. 51, No. 1 | 18 October 2008
- On perturbations of some constrained subspacesJournal of Computational and Applied Mathematics, Vol. 226, No. 1 | 1 Apr 2009
- An optimal approximation problem for a matrix equationInternational Journal of Computer Mathematics, Vol. 86, No. 2 | 1 Feb 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
- A Flexible and Efficient Algorithm for Regularized Fisher Discriminant AnalysisMachine Learning and Knowledge Discovery in Databases | 1 Jan 2009
- Computing the complete CS decompositionNumerical Algorithms, Vol. 50, No. 1 | 8 July 2008
- Generalized real perturbation values with applications to the structured real controllability radius of LTI systems2009 American Control Conference | 1 Jan 2009
- Combining transcriptional datasets using the generalized singular value decompositionBMC Bioinformatics, Vol. 9, No. 1 | 8 August 2008
- ANALYSIS OF SOLUTION FOR SUPERVISED GRAPH EMBEDDINGInternational Journal of Pattern Recognition and Artificial Intelligence, Vol. 22, No. 07 | 21 November 2011
- Least squares solutions to the equations with some constraintsApplied Mathematics and Computation, Vol. 204, No. 2 | 1 Oct 2008
- Generalized reflexive solutions of the matrix equation AXB=D and an associated optimal approximation problemComputers & Mathematics with Applications, Vol. 56, No. 6 | 1 Sep 2008
- Solution for supervised graph embedding: A case studySignal Processing, Vol. 88, No. 9 | 1 Sep 2008
- Amplify-and-forward relaying scheme based on GSVD for MIMO relay networks2008 International Conference on Neural Networks and Signal Processing | 1 Jun 2008
- The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximationJournal of Applied Mathematics and Computing, Vol. 27, No. 1-2 | 14 March 2008
- Idle State Detection in SSVEP-Based Brain-Computer Interfaces2008 2nd International Conference on Bioinformatics and Biomedical Engineering | 1 May 2008
- The (M,N)-symmetric Procrustes problemApplied Mathematics and Computation, Vol. 198, No. 1 | 1 Apr 2008
- A comparison of generalized linear discriminant analysis algorithmsPattern Recognition, Vol. 41, No. 3 | 1 Mar 2008
- A kernelized discriminant analysis algorithm based on modified generalized singular value decomposition2008 IEEE International Conference on Acoustics, Speech and Signal Processing | 1 Mar 2008
- Sliced Coordinate Analysis for Effective Dimension Reduction and Nonlinear ExtensionsJournal of Computational and Graphical Statistics, Vol. 17, No. 1 | 1 Mar 2008
- Incremental Linear Discriminant Analysis for Face RecognitionIEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol. 38, No. 1 | 1 Feb 2008
- The Generalized Singular Value Decomposition and the Method of Particular SolutionsSIAM Journal on Scientific Computing, Vol. 30, No. 3 | 21 March 2008
- Cluster-Preserving Dimension Reduction Methods for Document ClassificationSurvey of Text Mining II | 1 Jan 2008
- Generalized Canonical Correlation Analysis Using GSVD2008 International Symposium on Computer Science and Computational Technology | 1 Jan 2008
- Matrix equation AXB = E with PX = sXP constraintApplied Mathematics-A Journal of Chinese Universities, Vol. 22, No. 4 | 1 Dec 2007
- Discriminant Subspace Analysis: A Fukunaga-Koontz ApproachIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 29, No. 10 | 1 Oct 2007
- Improving implementation of linear discriminant analysis for the high dimension/small sample size problemComputational Statistics & Data Analysis, Vol. 52, No. 1 | 1 Sep 2007
- Inverse problems for nonsymmetric matrices with a submatrix constraintApplied Mathematics and Computation, Vol. 189, No. 2 | 1 Jun 2007
- The matrix equations with constraintApplied Mathematics and Computation, Vol. 189, No. 2 | 1 Jun 2007
- On the Gaussian MIMO Wiretap Channel2007 IEEE International Symposium on Information Theory | 1 Jun 2007
- Least-squares solutions of matrix inverse problem for bi-symmetric matrices with a submatrix constraintNumerical Linear Algebra with Applications, Vol. 14, No. 5 | 1 January 2007
- Inverse problems for symmetric matrices with a submatrix constraintApplied Numerical Mathematics, Vol. 57, No. 5-7 | 1 May 2007
- Least-Squares Solution with the Minimum-Norm for the Matrix Equation A T XB+B T X T A = D and Its ApplicationsActa Mathematicae Applicatae Sinica, English Series, Vol. 23, No. 2 | 1 Apr 2007
- The reflexive and anti-reflexive solutions of the matrix equation AHXB=CJournal of Computational and Applied Mathematics, Vol. 200, No. 2 | 1 Mar 2007
- A Partial Condition Number for Linear Least Squares ProblemsSIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 2 | 3 April 2007
- Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian SpectraSIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 1 | 21 December 2006
- A Perceptually Constrained GSVD-Based Approach for Enhancing Speech Corrupted by Colored NoiseIEEE Transactions on Audio, Speech and Language Processing, Vol. 15, No. 1 | 1 Jan 2007
- The expansion problem of anti-symmetric matrix under a linear constraint and the optimal approximationJournal of Computational and Applied Mathematics, Vol. 197, No. 1 | 1 Dec 2006
- The matrix nearness problem for symmetric matrices associated with the matrix equation [ATXA,BTXB]=[C,D]Linear Algebra and its Applications, Vol. 418, No. 2-3 | 1 Oct 2006
- Feature Reduction via Generalized Uncorrelated Linear Discriminant AnalysisIEEE Transactions on Knowledge and Data Engineering, Vol. 18, No. 10 | 1 Oct 2006
- Adaptive nonlinear discriminant analysis by regularized minimum squared errorsIEEE Transactions on Knowledge and Data Engineering, Vol. 18, No. 5 | 1 May 2006
- Solving the small sample size problem in face recognition using generalized discriminant analysisPattern Recognition, Vol. 39, No. 2 | 1 Feb 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
- Least-squares solution with the minimum-norm for the matrix equation (AXB, GXH) = (C, D)Computers & Mathematics with Applications, Vol. 50, No. 3-4 | 1 Aug 2005
- A Relationship between Linear Discriminant Analysis and the Generalized Minimum Squared Error SolutionSIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 2 | 31 July 2006
- Best Approximate Solution of Matrix Equation AXB+CYD=ESIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 3 | 31 July 2006
- The Generalized Eigenvalue Problem for Nonsquare Pencils Using a Minimal Perturbation ApproachSIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 2 | 31 July 2006
- A New Approach to Generalized Singular Value DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 2 | 31 July 2006
- 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
- The inverse problem of bisymmetric matrices with a submatrix constraintNumerical Linear Algebra with Applications, Vol. 11, No. 1 | 5 June 2003
- Cluster-Preserving Dimension Reduction Methods for Efficient Classification of Text DataSurvey of Text Mining | 1 Jan 2004
- Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organismsProceedings of the National Academy of Sciences, Vol. 100, No. 6 | 11 March 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
- Relationships among Various Kinds of Eigenvalue and Singular Value DecompositionsNew Developments in Psychometrics | 1 Jan 2003
- The Constrained Solutions of Two Matrix EquationsActa Mathematica Sinica, English Series, Vol. 18, No. 4 | 1 Oct 2002
- Regularization of Ill-Conditioned SystemsComputational Aspects of Linear Control | 1 Jan 2002
- On Accurate Quotient Singular Value Computation in Floating-Point ArithmeticSIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 3 | 31 July 2006
- Mathematics for modal analysisModal Analysis | 1 Jan 2001
- Some new properties of the equality constrained and weighted least squares problemLinear Algebra and its Applications, Vol. 320, No. 1-3 | 1 Nov 2000
- On a variational formulation of the QSVD and the RSVDLinear 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
- 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
- Methods and algorithms of solving spectral problems for polynomial and rational matricesJournal of Mathematical Sciences, Vol. 96, No. 3 | 1 Sep 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
- Generalized Singular Value Decomposition Approach for Consistent On-Line Dynamic Traffic AssignmentTransportation Research Record: Journal of the Transportation Research Board, Vol. 1667, No. 1 | 1 January 1999
- Verification Algorithms for Generalized Singular ValuesMathematische Nachrichten, Vol. 208, No. 1 | 20 September 2010
- Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problemLinear Algebra and its Applications, Vol. 280, No. 2-3 | 1 Sep 1998
- Perturbation analysis of the canonical subspacesLinear Algebra and its Applications, Vol. 279, No. 1-3 | 1 Aug 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
- On a Variational Formulation of the Generalized Singular Value DecompositionSIAM Journal on Matrix Analysis and Applications, Vol. 18, No. 4 | 31 July 2006
- Equivalent formulae for the supremum and stability of weighted pseudoinversesMathematics of Computation, Vol. 66, No. 220 | 1 January 1997
- Linear matrix equations from an inverse problem of vibration theoryLinear Algebra and its Applications, Vol. 246 | 1 Oct 1996
- Stochastic realization with exogenous inputs and ‘subspace-methods’ identificationSignal Processing, Vol. 52, No. 2 | 1 Jul 1996
- A Simple “Subspace” Identification Method with Exogenous InputsIFAC Proceedings Volumes, Vol. 29, No. 1 | 1 Jun 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
- Perturbation theory for orthogonal projection methods with applications to least squares and total least squaresLinear Algebra and its Applications, Vol. 234 | 1 Feb 1996
- Orthogonal projection and total least squaresNumerical Linear Algebra with Applications, Vol. 2, No. 2 | 1 Mar 1995
- 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
- 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
- On the Early History of the Singular Value DecompositionSIAM Review, Vol. 35, No. 4 | 12 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
- Subspace model identification Part 3. Analysis of the ordinary output-error state-space model identification algorithmInternational Journal of Control, Vol. 58, No. 3 | 1 Sep 1993
- A New Preprocessing Algorithm for the Computation of the Generalized Singular Value DecompositionSIAM Journal on Scientific Computing, Vol. 14, No. 4 | 13 July 2006
- On the QR algorithm and updating the SVD and the URV decomposition in parallelLinear Algebra and its Applications, Vol. 188-189 | 1 Jul 1993
- 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
- Ranks of Submatrices of a Matrix and Its InverseLinear Algebra for Large Scale and Real-Time Applications | 1 Jan 1993
- The symmetric solution of the matrix equations AX + YA = C, AXAT + BYBT = C, and (ATXA, BTXB) = (C, D)Linear Algebra and its Applications, Vol. 179 | 1 Jan 1993
- Algebraic relations between the total least squares and least squares problems with more than one solutionNumerische Mathematik, Vol. 62, No. 1 | 1 Dec 1992
- 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
- The Analysis for the Total Least Squares Problem with More Than One SolutionSIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 3 | 17 July 2006
- On the structure and geometry of the product singular value decompositionLinear Algebra and its Applications, Vol. 168 | 1 Apr 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
- The product-product singular value decomposition of matrix tripletsBIT, Vol. 31, No. 4 | 1 Dec 1991
- Generalizations of the singular value and QR decompositionsSignal Processing, Vol. 25, No. 2 | 1 Nov 1991
- A systolic algorithm for QSVD updatingSignal Processing, Vol. 25, No. 2 | 1 Nov 1991
- The Restricted Singular Value Decomposition: Properties and ApplicationsSIAM Journal on Matrix Analysis and Applications, Vol. 12, No. 3 | 17 July 2006
- 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
- Parallel Algorithms for Singular Value ProblemsNumerical Linear Algebra, Digital Signal Processing and Parallel Algorithms | 1 Jan 1991
- SVD-based subspace methods for multivariable continuous-time systems identificationIdentification of Continuous-Time Systems | 1 Jan 1991
- On the Use of the Singular Value Decomposition in Identification and Signal ProcessingNumerical Linear Algebra, Digital Signal Processing and Parallel Algorithms | 1 Jan 1991
- The discrete picard condition for discrete ill-posed problemsBIT, Vol. 30, No. 4 | 1 Dec 1990
- On the symmetric solutions of linear matrix equationsLinear Algebra and its Applications, Vol. 131 | 1 Apr 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
- An algorithm for computing the spectral structure of a singular linear matrix pencilJournal of Soviet Mathematics, Vol. 47, No. 6 | 1 Dec 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
- Symmetric solutions of linear matrix equations by matrix decompositionsLinear Algebra and its Applications, Vol. 119 | 1 Jul 1989
- Numerical treatment of restricted gauss-markov model 1Communications in Statistics - Simulation and Computation, Vol. 17, No. 2 | 1 Jan 1988
- Singular value and generalized singular value decompositions and the solution of linear matrix equationsLinear Algebra and its Applications, Vol. 88-89 | 1 Apr 1987
- Computing the CS-Decomposition on Systolic ArraysSIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 4 | 14 July 2006
- 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
- Stably Computing the Kronecker Structure and Reducing Subspaces of Singular Pencils A-λ for Uncertain DataLarge Scale Eigenvalue Problems, Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems | 1 Jan 1986
- Computing the CS and the generalized singular value decompositionsNumerische Mathematik, Vol. 46, No. 4 | 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
- A parallel method for computing the generalized singular value decompositionJournal of Parallel and Distributed Computing, Vol. 2, No. 3 | 1 Aug 1985
- The singular value decomposition in multivariate statisticsACM SIGNUM Newsletter, Vol. 20, No. 3 | 1 July 1985
- Linear unbiased approximators of the disturbances in the standard linear modelLinear Algebra and its Applications, Vol. 67 | 1 Jun 1985
- The generalized singular value decomposition and the general (A-λB)-problemBIT, Vol. 24, No. 4 | 1 Dec 1984
- A Note on a Result of Sun Ji-Guang: Sensitivity of the CS and GSV DecompositionsSIAM Journal on Numerical Analysis, Vol. 21, No. 1 | 17 July 2006
- 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
- On Complex Rational ApproximationComputational Aspects of Complex Analysis | 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
- Computing theCS decomposition of a partitioned orthonormal matrixNumerische Mathematik, Vol. 40, No. 3 | 1 Oct 1982
- The impact of the singular value decomposition in system theory, signal processing, and circuit theoryThree Decades of Mathematical System Theory
- Subspace algorithms for the stochastic identification problem[1991] Proceedings of the 30th 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
- ESPRIT and TAM (Toeplitz approximation method) are theoretically equivalentICASSP-88., International Conference on Acoustics, Speech, and Signal 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)
- On the common structure of several well-known methods for harmonic analysis a direction-of-arrival estimation induced by a new version of ESPRITFourth Annual ASSP Workshop on Spectrum Estimation and Modeling
- 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)