3. Edition - July 2010
102.- Euro
2010. 664 Pages, Hardcover
ISBN-10: 0-470-52833-8
ISBN-13: 978-0-470-52833-4 - John Wiley & Sons








Short 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 MATLAB(r) 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.

From the contents
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(r) Terms.