Fundamentals of Matrix Computations

ISBN-10: 0470528338
ISBN-13: 9780470528334
Edition: 3rd 2010
Authors: David S. Watkins
List price: $88.50
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Description: Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. Featuring many new and updated examples and exercises that use the MATLABr language, this  More...

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Book details

List price: $88.50
Edition: 3rd
Copyright year: 2010
Publisher: John Wiley & Sons, Limited
Publication date: 7/20/2010
Binding: Hardcover
Pages: 664
Size: 6.50" wide x 9.75" long x 1.75" tall
Weight: 2.574
Language: English

Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. Featuring many new and updated examples and exercises that use the MATLABr language, this revision presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work. It also includes modern coverage of Singular Value Decomposition, a streamlined discussion of the Gram-Schmidt process, and a discussion on balancing the eigenvalue problem. Practicing scientists and graduate and advanced undergraduate students will find this popular book more than meets their needs.

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
Francis's Algorithm
Use of Francis's Algorithm to Calculate Eigenvectors
The SVD Revisited
Eigenvalues and Eigenvectors II
Eigenspaces and Invariant Subspaces
Subspace Iteration and Simultaneous Iteration
Krylov Subspaces and Francis's Algorithm
Large Sparse Eigenvalue Problems
Implicit Restarts
The Jacobi-Davidson and Related Algorithms
Eigenvalues and Eigenvectors III
Sensitivity of Eigenvalues and Eigenvectors
Methods for the Symmetric Eigenvalue Problem
Product Eigenvalue Problems
The Generalized Eigenvalue Problem
Iterative Methods for Linear Systems
A Model Problem
The Classical Iterative Methods
Convergence of Iterative Methods
Descent Methods; Steepest Descent
On Stopping Criteria
Preconditioners
The Conjugate-Gradient Method
Derivation of the CG Algorithm
Convergence of the CG Algorithm
Indefinite and Nonsymmetric Problems
References
Index
Index of MATLAB� Terms

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