Introduction To Matrix Computations

Author : G. W. Stewart
Publisher : Elsevier
Page : 457 pages
File Size : 47,7 Mb
Release : 1973-06-15
Category : Mathematics
ISBN : 9780080926148

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Introduction to Matrix Computations by G. W. Stewart Pdf

Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra.

Author : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 734 pages
File Size : 41,5 Mb
Release : 1996-10-15
Category : Mathematics
ISBN : 0801854148

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Matrix Computations by Gene H. Golub,Charles F. Van Loan Pdf

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.

Author : Gilbert W. Stewart
Publisher : Unknown
Page : 441 pages
File Size : 49,8 Mb
Release : 1990
Category : Matrices
ISBN : OCLC:312049540

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Introduction to Matrix Computations by Gilbert W. Stewart Pdf

Author : Gene Howard Golub
Publisher : Unknown
Page : 694 pages
File Size : 54,8 Mb
Release : 1996
Category : Matrices
ISBN : 0801837391

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Matrix Computations by Gene Howard Golub Pdf

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.

Author : David S. Watkins
Publisher : Unknown
Page : 476 pages
File Size : 50,9 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : STANFORD:36105031244911

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Fundamentals of Matrix Computations by David S. Watkins Pdf

The use of numerical methods continues to expand rapidly. At their heart lie matrix computations. Written in a clear, expository style, it allows students and professionals to build confidence in themselves by putting the theory behind matrix computations into practice instantly. Algorithms that allow students to work examples and write programs introduce each chapter. The book then moves on to discuss more complicated theoretical material. Using a step-by-step approach, it introduces mathematical material only as it is needed. Exercises range from routine computations and verifications to extensive programming projects and challenging proofs.

Author : Thomas F. Coleman,Charles Van Loan
Publisher : SIAM
Page : 271 pages
File Size : 41,8 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 1611971047

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Handbook for Matrix Computations by Thomas F. Coleman,Charles Van Loan Pdf

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.

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 52,7 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Author : David S. Watkins
Publisher : John Wiley & Sons
Page : 635 pages
File Size : 50,5 Mb
Release : 2004-08-27
Category : Mathematics
ISBN : 9780471461678

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Fundamentals of Matrix Computations by David S. Watkins Pdf

A significantly revised and improved introduction to a critical aspect of scientific computation Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights. This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes: * Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations * Early introduction of the singular value decomposition * A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems * An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.

Author : John Rischard Rice
Publisher : McGraw-Hill Companies
Page : 280 pages
File Size : 52,6 Mb
Release : 1981
Category : Computers
ISBN : UOM:39015000961592

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Matrix Computations and Mathematical Software by John Rischard Rice Pdf

Linear algebra background; types and sources of matrix computational problems; type of matrix that arise; gauss elimination and LU factorization; mathematical software objectives; mathematical software performance evaluation; how do you know you have right answers?; conditioning and backward error analysis; iterative methods; linear least squares and regression; projects; standard linear algebra software.

Author : Alan J. Laub
Publisher : SIAM
Page : 157 pages
File Size : 43,5 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9781611972214

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Computational Matrix Analysis by Alan J. Laub Pdf

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.

Author : Dingyü Xue
Publisher : Walter de Gruyter GmbH & Co KG
Page : 223 pages
File Size : 40,5 Mb
Release : 2020-03-23
Category : Computers
ISBN : 9783110663716

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Linear Algebra and Matrix Computations with MATLAB® by Dingyü Xue Pdf

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.

Author : Nabil Nassif,Jocelyne Erhel,Bernard Philippe
Publisher : CRC Press
Page : 258 pages
File Size : 45,7 Mb
Release : 2015-06-24
Category : Mathematics
ISBN : 9781482258714

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Introduction to Computational Linear Algebra by Nabil Nassif,Jocelyne Erhel,Bernard Philippe Pdf

Teach Your Students Both the Mathematics of Numerical Methods and the Art of Computer ProgrammingIntroduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations. The book is designed for senior undergraduate stud

Author : Victor Y. Pan
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201298

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Structured Matrices and Polynomials by Victor Y. Pan Pdf

This user-friendly, engaging textbook makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.

Author : Charles F. Van Loan
Publisher : Pearson
Page : 388 pages
File Size : 48,8 Mb
Release : 2000
Category : Computers
ISBN : STANFORD:36105028540362

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Introduction to Scientific Computing by Charles F. Van Loan Pdf

Unique in content and approach, this book covers all the topics that are usually covered in an introduction to scientific computing--but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the "connection" between continuous mathematics and computing. "MATLAB 5" is used "throughout" to encourage experimentation, and each chapter focuses on a different important theorem--allowing readers to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a "hard" problem that involves ill-conditioning, high dimension, etc.; 2)at least one theorem with both a rigorous proof and a "proof by MATLAB" experiment to bolster intuition; 3)at least one recursive algorithm; and 4)at least one connection to a real-world application. The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing. Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem. For engineers and mathematicians.

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 47,7 Mb
Release : 2007-07-27
Category : Computers
ISBN : 9780387708720

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Matrix Algebra by James E. Gentle Pdf

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.