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Fundamentals of Matrix Computations 2nd Edition by David Watkins ISBN 0471461678 9780471461678

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Fundamentals of Matrix Computations Second Edition David S. Watkins(Auth.) Digital Instant Download

Author(s): David S. Watkins(auth.), Myron B. Allen, David A. Cox, Peter Lax(eds.)
ISBN(s): 9780471249719, 0471249718
File Details: PDF, 5.17 MB
Year: 2002
Language: english
SKU: EB-4304776 Category: Tags: , , ,

Fundamentals of Matrix Computations 2nd Edition by David Watkins – Ebook PDF Instant Download/Delivery: 0471461678 , 9780471461678
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Cover image: Fundamentals of Matrix Computations
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ISBN 10: 0471461678
ISBN 13: 9780471461678
Author: David Watkins

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.

Fundamentals of Matrix Computations 2nd Table of contents:

1 Gaussian Elimination and Its Variants

1.1 Matrix Multiplication

1.2 Systems of Linear Equations

1.3 Triangular Systems

1.4 Positive Definite Systems; Cholesky Decomposition

1.5 Banded Positive Definite Systems

1.6 Sparse Positive Definite Systems

1.7 Gaussian Elimination and the LU Decomposition

1.8 Gaussian Elimination with Pivoting

1.9 Sparse Gaussian Elimination

2 Sensitivity of Linear Systems

2.1 Vector and Matrix Norms

2.2 Condition Numbers

2.3 Perturbing the Coefficient Matrix

2.4 A Posteriori Error Analysis Using the Residual

2.5 Roundoff Errors; Backward Stability

2.6 Propagation of Roundoff Errors

2.7 Backward Error Analysis of Gaussian Elimination

2.8 Scaling

2.9 Componentwise Sensitivity Analysis

3 The Least Squares Problem

3.1 The Discrete Least Squares Problem

3.2 Orthogonal Matrices, Rotators, and Reflectors

3.3 Solution of the Least Squares Problem

3.4 The Gram-Schmidt Process

3.5 Geometric Approach

3.6 Updating the QR Decomposition

4 The Singular Value Decomposition

4.1 Introduction

4.2 Some Basic Applications of Singular Values

4.3 The SVD and the Least Squares Problem

4.4 Sensitivity of the Least Squares Problem

5 Eigenvalues and Eigenvectors I

5.1 Systems of Differential Equations

5.2 Basic Facts

5.3 The Power Method and Some Simple Extensions

5.4 Similarity Transforms

5.5 Reduction to Hessenberg and Tridiagonal Forms

5.6 The QR Algorithm

5.7 Implementation of the QR algorithm

5.8 Use of the QR Algorithm to Calculate Eigenvectors

5.9 The SVD Revisited

6 Eigenvalues and Eigenvectors II

6.1 Eigenspaces and Invariant Subspaces

6.2 Subspace Iteration, Simultaneous Iteration, and the QR Algorithm

6.3 Eigenvalues of Large, Sparse Matrices, I

6.4 Eigenvalues of Large, Sparse Matrices, II

6.5 Sensitivity of Eigenvalues and Eigenvectors

6.6 Methods for the Symmetric Eigenvalue Problem

6.7 The Generalized Eigenvalue Problem

7 Iterative Methods for Linear Systems

7.1 A Model Problem

7.2 The Classical Iterative Methods

7.3 Convergence of Iterative Methods

7.4 Descent Methods; Steepest Descent

7.5 Preconditioners

7.6 The Conjugate-Gradient Method

7.7 Derivation of the CG Algorithm

7.8 Convergence of the CG Algorithm

7.9 Indefinite and Nonsymmetric Problems

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