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Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser.: Fundamentals of Matrix Computations by David S. Watkins (2010, Hardcover)

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Product Information

This Third Edition explains how to perform matrix computations efficiently and accurately by providing a detailed introduction to the fundamental ideas of numerical linear algebra and utilizes MATLAB® to perform elaborate computational experiments.

Product Identifiers

Publisher
Wiley & Sons, Incorporated, John
ISBN-10
0470528338
ISBN-13
9780470528334
eBay Product ID (ePID)
80517212

Product Key Features

Author
David S. Watkins
Publication Name
Fundamentals of Matrix Computations
Format
Hardcover
Language
English
Publication Year
2010
Series
Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser.
Type
Textbook
Number of Pages
664 Pages

Dimensions

Item Length
9.3in
Item Height
1.6in
Item Width
6.4in
Item Weight
37.7 Oz

Additional Product Features

Series Volume Number
94
Lc Classification Number
Qa188.W38 2010
Edition Number
3
Table of Content
Preface. Acknowledgments. 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 Gaussain Elimination and 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 Square 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 Francis's Algorithm. 5.7 Use of Francis's Algorithm to Calculate Eigenvectors. 5.8 The SVD Revisted. 6 Eigenvalues and Eigenvectors II. 6.1 Eigenspaces and Invariant Subspaces. 6.2 Subspace Iteration and Simultaneous Iteration. 6.3 Krylov Subspaces and Francis's Algorithm. 6.4 Large Sparse Eigenvalue Problems. 6.5 Implicit Restarts. 6.6 The Jacobi-Davidson and Related Algorithms. 7 Eigenvalues and Eigenvectors III. 7.1 Sensitivity of Eigenvalues and Eigenvectors. 7.2 Methods for the Symmetric Eigenvalue Problem. 7.3 Product Eigenvalue Problems. 7.4 The Generalized Eigenvalue Problem. 8 Iterative Methods for Linear Systems. 8.1 A Model Problem. 8.2 The Classical Iterative Methods. 8.3 Convergence of Iterative Methods. 8.4 Descent Methods; Steepest Descent. 8.5 On Stopping Criteria. 8.6 Preconditioners. 8.7 The Conjugate-Gradient Method. 8.8 Derivation of the CG Algorithm. 8.9 Convergence of the CG Algorithm. 8.10 Indefinite and Nonsymmetric Problems. References. Index. Index of MATLAB Terms.
Copyright Date
2010
Topic
Algebra / Linear, Matrices
Lccn
2010-001933
Dewey Decimal
512.9/434
Intended Audience
Scholarly & Professional
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics