Matrix Analysis and Computations

Matrix Analysis and Computations PDF

Author: Zhong-Zhi Bai

Publisher: SIAM

Published: 2021-09-09

Total Pages: 496

ISBN-13: 1611976634

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This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics

Matrix Algebra

Matrix Algebra PDF

Author: James E. Gentle

Publisher: Springer Science & Business Media

Published: 2007-07-27

Total Pages: 536

ISBN-13: 0387708723

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Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Numerical Methods in Matrix Computations

Numerical Methods in Matrix Computations PDF

Author: Åke Björck

Publisher: Springer

Published: 2014-10-07

Total Pages: 812

ISBN-13: 3319050893

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Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Handbook for Matrix Computations

Handbook for Matrix Computations PDF

Author: Thomas F. Coleman

Publisher: SIAM

Published: 1988-01-01

Total Pages: 271

ISBN-13: 9781611971040

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Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.

Computational Matrix Analysis

Computational Matrix Analysis PDF

Author: Alan J. Laub

Publisher: SIAM

Published: 2012-01-01

Total Pages: 157

ISBN-13: 9781611972214

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Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition estimation in book form for the first time; and an overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic; discussion and examples of conditioning, stability, and rounding analysis; an introduction to mathematical software topics related to numerical linear algebra; a thorough introduction to Gaussian elimination, along with condition estimation techniques; coverage of linear least squares, with orthogonal reduction and QR factorization; variants of the QR algorithm; and applications of the discussed algorithms.

Polynomial and Matrix Computations

Polynomial and Matrix Computations PDF

Author: Dario Bini

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 433

ISBN-13: 1461202655

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Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.

Linear Algebra and Matrix Computations with MATLAB®

Linear Algebra and Matrix Computations with MATLAB® PDF

Author: Dingyü Xue

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-03-23

Total Pages: 223

ISBN-13: 3110663716

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The book focused on solving linear algebra practical problems with MATLAB. The input and manipulation of matrices are introduced first, followed by the matrix analysis and transformation problem solutions. Matrix equation solutions, matrix function evaluations, and various linear algebra applications are also demonstrated. With extensive exercises, the book sets up a new viewpoint for the readers in understanding linear algebra problems.

Matrix Computations

Matrix Computations PDF

Author: Gene H. Golub

Publisher: JHU Press

Published: 1996-10-15

Total Pages: 734

ISBN-13: 9780801854149

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Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

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