Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Purchase Benefits
What is included with this book?
Preface | p. ix |
Acknowledgments | p. xv |
Gaussian Elimination and Its Variants | p. 1 |
Matrix Multiplication | p. 1 |
Systems of Linear Equations | p. 12 |
Triangular Systems | p. 24 |
Positive Definite Systems; Cholesky Decomposition | p. 33 |
Banded Positive Definite Systems | p. 55 |
Sparse Positive Definite Systems | p. 64 |
Gaussian Elimination and the LU Decomposition | p. 71 |
Gaussian Elimination with Pivoting | p. 94 |
Sparse Gaussian Elimination | p. 107 |
Sensitivity of Linear Systems | p. 113 |
Vector and Matrix Norms | p. 114 |
Condition Numbers | p. 122 |
Perturbing the Coefficient Matrix | p. 133 |
A Posteriori Error Analysis Using the Residual | p. 137 |
Roundoff Errors; Backward Stability | p. 139 |
Propagation of Roundoff Errors | p. 149 |
Backward Error Analysis of Gaussian Elimination | p. 157 |
Scaling | p. 171 |
Componentwise Sensitivity Analysis | p. 176 |
The Least Squares Problem | p. 183 |
The Discrete Least Squares Problem | p. 183 |
Orthogonal Matrices, Rotators, and Reflectors | p. 187 |
Solution of the Least Squares Problem | p. 215 |
The Gram-Schmidt Process | p. 223 |
Geometric Approach | p. 238 |
Updating the QR Decomposition | p. 247 |
The Singular Value Decomposition | p. 259 |
Introduction | p. 260 |
Some Basic Applications of Singular Values | p. 264 |
The SVD and the Least Squares Problem | p. 273 |
Sensitivity of the Least Squares Problem | p. 279 |
Eigenvalues and Eigenvectors I | p. 289 |
Systems of Differential Equations | p. 289 |
Basic Facts | p. 305 |
The Power Method and Some Simple Extensions | p. 314 |
Similarity Transforms | p. 334 |
Reduction to Hessenberg and Tridiagonal Forms | p. 350 |
Francis's Algorithm | p. 358 |
Use of Francis's Algorithm to Calculate Eigenvectors | p. 386 |
The SVD Revisited | p. 389 |
Eigenvalues and Eigenvectors II | p. 409 |
Eigenspaces and Invariant Subspaces | p. 410 |
Subspace Iteration and Simultaneous Iteration | p. 420 |
Krylov Subspaces and Francis's Algorithm | p. 428 |
Large Sparse Eigenvalue Problems | p. 437 |
Implicit Restarts | p. 456 |
The Jacobi-Davidson and Related Algorithms | p. 466 |
Eigenvalues and Eigenvectors III | p. 471 |
Sensitivity of Eigenvalues and Eigenvectors | p. 471 |
Methods for the Symmetric Eigenvalue Problem | p. 485 |
Product Eigenvalue Problems | p. 511 |
The Generalized Eigenvalue Problem | p. 526 |
Iterative Methods for Linear Systems | p. 545 |
A Model Problem | p. 546 |
The Classical Iterative Methods | p. 554 |
Convergence of Iterative Methods | p. 568 |
Descent Methods; Steepest Descent | p. 583 |
On Stopping Criteria | p. 594 |
Preconditioners | p. 596 |
The Conjugate-Gradient Method | p. 602 |
Derivation of the CG Algorithm | p. 607 |
Convergence of the CG Algorithm | p. 615 |
Indefinite and Nonsymmetric Problems | p. 621 |
References | p. 627 |
Index | p. 635 |
Index of MATLAB® Terms | p. 643 |
Table of Contents provided by Ingram. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.