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Issue 4 | 1990 | pp. 537-722

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1990

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Select this Article		Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis A. C. Lazer and P. J. McKenna SIAM Rev. 32, pp. 537-578 (42 pages) \| Cited 63 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract This paper surveys an area of nonlinear functional analysis and its applications. The main application is to the existence and multiplicity of periodic solutions of a possible mathematical models of nonlinearly supported bending beams, and their possible application to nonlinear behavior as observed in large-amplitude flexings in suspension bridges. A second area, periodic flexings in a floating beam, also nonlinearly supported, is covered at the end of the paper.

Select this Article		Stochastic Perturbation Theory G. W. Stewart SIAM Rev. 32, pp. 579-610 (32 pages) \| Cited 16 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a first-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variation in the perturbed quantity. Up to the higher-order terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares and the eigenvalue problem.

Select this Article		The Convergence of Linear Stationary Iterative Processes for Solving Singular Unstructured Systems of Linear Equations Achiya Dax SIAM Rev. 32, pp. 611-635 (25 pages) \| Cited 17 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract This paper reviews the convergence properties of linear stationary iterative processes for solving large unstructured systems of linear equations. Special attention is given to the case where the system to be solved is singular and possibly inconsistent. The review starts by investigating the iteration ${\bf x}_{k + 1} = H{\bf x}_k + {\bf f},\, k = 0,1,2, \cdots $, when the system $(I - H){\bf x} = {\bf f}$ is inconsistent. In this case the sequence $\left\{ {\bf x_k } \right\}$ always diverges. Nevertheless, when $H$ is “convergent” there exists a vector ${\bf q} \in \,{\text{Null}}(I - H)$ such that the sequence $\hat {\bf x}_k = {\bf x}_k - k{\bf q}$ converges. The limit of this sequence, $\hat {\bf x}$, solves a certain least-squares problem, and the sequence of residual vectors, ${\bf r}_k = (I - H){\bf x}_k - {\bf f}$, converges to $(I - H)\hat {\bf x} - {\bf f}$. Furthermore, if $H$ is similar to a real diagonal matrix then the corresponding norms of ${\bf r}_k $ and $\hat {\bf x}_k - \hat {\bf x}$ decreases monotonically. More can be said when ${\bf x}_0 \in {\text{Range}}(I - H)$. There are several iterative methods for solving a symmetric positive semidefinite system of linear equations, $G{\bf x} = {\bf h}$, that have the form ${\bf x}_{k + 1} = Q^{ - 1} (Q - G){\bf x}_k + Q^{ - 1} {\bf h}$. Here the iteration matrix, $H = Q^{ - 1} (Q - G)$, is convergent whenever the matrix $P = Q + Q^T - G$ is positive definite. In this case we obtain the surprising result that the sequence of residuals, $\{ G{\bf x}_k - {\bf h}\} $, converges even when the system $G{\bf x} = {\bf h}$ is inconsistent. The developed theory reveals interesting properties of the “basic” iterative methods (e.g., Richardson’s method, Jacobi’s method, SOR, and SSOR) with minimal assumptions on the structure of $G$. For example, if $H$ is convergent and symmetric as with Richardson’s method, then the sequences $\{ \|\|\hat {\bf x}_k - \hat {\bf x}\|\|\} $ and $\{ \|\|G{\bf x}_k - {\bf h}\|\|\} $ decrease monotonically, and the sequence $\{ G{\bf x}_k - {\bf h}\} $ converges to $G\hat {\bf x} - {\bf h}$, where $\hat {\bf x}$ solves the least-squares problem: minimize $\|\|{\bf Gx}_k - {\bf h}\|\|^2 $. Moreover, if ${\bf x}_0 \in {\text{Range}}(G)$ and the system $(I - H){\bf x} = {\bf f}$ is solvable, then the sequence $\{ {\bf x}_k \} $ converges to the minimum-norm solution of this system. The paper ends with a discussion of iterative methods for solving a general linear system, $A{\bf x} = {\bf b}$, where $A$ is large, sparse, and unstructured. These methods can be divided into two classes. One is aimed at solving the normal equations $A^T A{\bf x} = A^T {\bf b}$ (e.g., column SOR or Cimmino’s method), and one is aimed at solving the Björck–Elfving equations ${\bf x} = A^T {\bf y}$ and $AA^T {\bf y} = {\bf b}$ (e.g., Kaczmarz’s method). It is shown that in both cases the theory developed for symmetric positive semidefinite systems enables us to characterize the behavior of the methods and to derive simplified proofs of convergence.

Select this Article		Code Recognition with Neural Network Dynamical Systems Clark Jeffries SIAM Rev. 32, pp. 636-651 (16 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract A class of dynamical systems called neural networks can be used to solve a variety of finite choice problems including the problem of correcting binary code.

Select this Article		Nonlinear Phenomena in a Column of Liquid in a Rotating Manometer S. Graham Kelly SIAM Rev. 32, pp. 652-659 (8 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract The stationary configuration of a column of liquid in a U-tube manometer rotating about an axis other than its axis of symmetry is predicted using a pressure distribution derived from Euler’s equation and from the governing differential equation of motion. Nonlinear behavior is evident in that the stationary position of the liquid air interface will “jump” at critical values of the speed of rotation. A hysteresis effect is predicted in that the “jump” occurs at a different speed if the speed is being decreased rather than increased. Analysis defines regions of stable and unstable stationary positions.

Select this Article		Convective Diffusion in Two-Dimensional Incompressible Linear Flow Peter S. Bernard SIAM Rev. 32, pp. 660-666 (7 pages) \| Cited 2 times Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract An exact solution for the Green’s function governing convective diffusion in two-dimensional, linear, incompressible flow is computed by elementary means.

Select this Article		Generalization of the “universal pivot function” and its use in constructing confidence intervals and sets John E. Angus SIAM Rev. 32, pp. 667-670 (4 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
	+ -	Show Abstract This paper gives a general method of constructing confidence intervals or sets for a real parameter $\theta $ based on a slight generalization of the usual “pivot function” approach taken in undergraduate statistics courses. The method is generally applicable and leads to the usual confidence intervals for the standard problems.

Select this Article		Addendum: Stokes Flow: An Elementary Treatment Michael A. B. Deakin SIAM Rev. 32, pp. 671-671 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Simultaneous Functional Equations Paul Schweitzer SIAM Rev. 32, pp. 672-672 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Exponentially Windowed Estimates of a Periodically Sampled Time-Series, and Its First and Second Derivatives Using Quadratic Regression Ken Lever SIAM Rev. 32, pp. 672-673 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Orthogonal Matrices and the Matrix Exponential Dennis S. Bernstein SIAM Rev. 32, pp. 673-673 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Cyclic Pursuit with Lead Angle M. S. Klamkin SIAM Rev. 32, pp. 673-673 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Cyclic Pursuit with Lead Angle (Quickie) SIAM Rev. 32, pp. 674-674 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Late Solutions D. P. Laurie and B. Tibken SIAM Rev. 32, pp. 674-674 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		The Complexity of the Standard Form of an Integer (K. V. Lever) Robert E. Terrell and H. L. Abbott SIAM Rev. 32, pp. 674-681 (8 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Two Determinant Inequalities (Ralph Kelsey) Michael Renardy SIAM Rev. 32, pp. 681-682 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		On the Number of Roots of a Transcendental Equation D. K. Cohoon, R. M. Purcell, Michael Renardy, and C. C. Grosjean SIAM Rev. 32, pp. 682-683 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Complement of Weber’s Integral (J. W. Miles) Norbert Ortner and M. L. Glasser SIAM Rev. 32, pp. 683-684 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		A Functional Equation (David W. Wilson) D. G. Rogers and Peter Borwein SIAM Rev. 32, pp. 684-686 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Probabilistic Ethics Ted W. Lockhart, Robert Ingle, and Peter Wollan SIAM Rev. 32, pp. 686-688 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Generalized Concavity (Mordecai Avriel, Walter E. Diewert, Siegfried Schaible, and Israel Zang) Jonathan Borwein SIAM Rev. 32, pp. 689-690 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Matrix Computations; Second Edition (Gene Golub and Charles F. Van Loan) James W. Demmel SIAM Rev. 32, pp. 690-691 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Low-Gravity Fluid Mechanics: Mathematical Theory of Capillary Phenomena (A. D. Myshkis, V. G. Babskii, N. D. Kopachevskii, L. A. Slobozhanin, and A. D. Tyuptsov; R. S. Wadhwa, trans.) Hendrik A. Dijkstra SIAM Rev. 32, pp. 691-693 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Percolation (Geoffrey Grimmett) Richard T. Durrett SIAM Rev. 32, pp. 693-693 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Vibration and Coupling of Continuous Systems: Asymptotic Methods (Jacqueline Sanchez Hubert and Enrique Sanchez Palencia) Alp Eden SIAM Rev. 32, pp. 693-694 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Control of Partially-Known Dynamical Systems (A. A. Bahnasawi and M. S. Mahmoud) Ali Feliachi SIAM Rev. 32, pp. 694-695 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Rational Kinematics (Jorge Angeles) Ferdinand Freudenstein SIAM Rev. 32, pp. 695-696 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Variational Principles of Continuum Mechanics with Engineering Applications. Volume 2: Introduction to Optimal Design Theory (Vadim Komkov) J. Haug Edward SIAM Rev. 32, pp. 696-697 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Computational Hydraulics: An Introduction (Cornelis B. Vreugdenhil) K.-Peter Holz SIAM Rev. 32, pp. 697-698 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Elements of Differentiable Dynamics and Bifurcation Theory (David Ruelle) Nicholas D. Kazarinoff SIAM Rev. 32, pp. 698-698 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Polynomials (E. J. Barbeau) M. S. Klamkin SIAM Rev. 32, pp. 699-700 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Introduction to Numerical Linear Algebra and Optimisation (Philippe G. Ciarlet with Bernadette Miara and Jean-Marie Thomas; A. Buttigieg, trans.) John C. Nash SIAM Rev. 32, pp. 700-702 (3 pages) \| Cited 1 time Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Fundamentals of Pattern Recognition (Monique Pavel) Yoh-Han Pao SIAM Rev. 32, pp. 702-702 (1 page) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Analysis of Skeletal Structural Systems in the Elastic and Elastic-Plastic Range (Adam Borkowski) E. Bruce Pitman SIAM Rev. 32, pp. 702-703 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Initial-Boundary Value Problems and the Navier-Stokes Equations (Heinz-Otto Kreiss and Jens Lorenz) Gustavo Ponce SIAM Rev. 32, pp. 703-704 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Judea Pearl) F. J. Radermacher SIAM Rev. 32, pp. 704-707 (4 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Continuous Decoupling Transformations for Linear Boundary Value Problems (P. M. van Loon) R. D. Russell SIAM Rev. 32, pp. 707-708 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Large Scale Systems: Decentralization, Structure Constraints and Fixed Modes (L. Trave, A. Titli, and A. Tarras) M. Erol Sezer SIAM Rev. 32, pp. 708-709 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Other Books Received SIAM Rev. 32, pp. 709-717 (9 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		New Members SIAM Rev. 32, pp. 718-720 (3 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

Select this Article		Report of the Treasurer for the Year Ended December 31, 1989 SIAM Rev. 32, pp. 721-722 (2 pages) Online Publication Date: July 18, 2006 Full Text: \| Download PDF
		Abstract Unavailable

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