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Fundamentals of Matrix Computations

ISBN-10: 0471614149

ISBN-13: 9780471614142

Edition: 1991

Authors: David S. Watkins

List price: $98.95
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Book details

List price: $98.95
Copyright year: 1991
Publisher: John Wiley & Sons, Incorporated
Publication date: 1/16/1991
Binding: Hardcover
Pages: 449
Size: 7.25" wide x 10.25" long x 1.25" tall
Weight: 2.244
Language: English

Preface
Acknowledgments
Gaussian Elimination and Its Variants
Matrix Multiplication
Systems of Linear Equations
Triangular Systems
Positive Definite Systems: Cholesky Decomposition
Banded Positive Definite Systems
Sparse Positive Definite Systems
Gaussian Elimination and the LU Decomposition
Gaussian Elimination with Pivoting
Sparse Gaussian Elimination
Sensitivity of Linear Systems
Vector and Matrix Norms
Condition Numbers
Perturbing the Coefficient Matrix
A Posteriori Error Analysis Using the Residual
Roundoff Errors; Backward Stability
Propagation of Roundoff Errors
Backward Error Analysis of Gaussian Elimination
Scaling
Componentwise Sensitivity Analysis
The Least Squares Problem
The Discrete Least Squares Problem
Orthogonal Matrices, Rotators, and Reflectors
Solution of the Least Squares Problem
The Gram-Schmidt Process
Geometric Approach
Updating the QR Decomposition
The Singular Value Decomposition
Introduction
Some Basic Applications of Singular Values
The SVD and the Least Squares Problem
Sensitivity of the Least Squares Problem
Eigenvalues and Eigenvectors I
Systems of Differential Equations
Basic Facts
The Power Method and Some Simple Extensions
Similarity Transforms
Reduction to Hessenberg and Tridiagonal Forms
The QR Algorithm
Implementation of the QR algorithm
Use of the QR Algorithm to Calculate Eigenvectors
The SVD Revisited
Eigenvalues and Eigenvectors II
Eigenspaces and Invariant Subspaces
Subspace Iteration, Simultaneous Iteration, and the QR Algorithm
Eigenvalues of Large, Sparse Matrices, I
Eigenvalues of Large, Sparse Matrices, II
Sensitivity of Eigenvalues and Eigenvectors
Methods for the Symmetric Eigenvalue Problem
The Generalized Eigenvalue Problem
Iterative Methods for Linear Systems
A Model Problem
The Classical Iterative Methods
Convergence of Iterative Methods
Descent Methods; Steepest Descent
Preconditioners
The Conjugate-Gradient Method
Derivation of the CG Algorithm
Convergence of the CG Algorithm
Indefinite and Nonsymmetric Problems
Some Sources of Software for Matrix Computations
References
Index
Index of Matlab Terms