| Preface | p. xi |
| Global References | p. xiii |
| Other Books | p. xv |
| Useful URLs | p. xix |
| Common Notation | p. xxi |
| Matrix Multiplication | p. 1 |
| Basic Algorithms and Notation | p. 2 |
| Structure and Efficiency | p. 14 |
| Block Matrices and Algorithms | p. 22 |
| Fast Matrix-Vector Products | p. 33 |
| Vectorization and Locality | p. 43 |
| Parallel Matrix Multiplication | p. 49 |
| Matrix Analysis | p. 63 |
| Basic Ideas from Linear Algebra | p. 64 |
| Vector Norms | p. 68 |
| Matrix Norms | p. 71 |
| The Singular Value Decomposition | p. 76 |
| Subspace Metrics | p. 81 |
| The Sensitivity of Square Systems | p. 87 |
| Finite Precision Matrix Computations | p. 93 |
| General Linear Systems | p. 105 |
| Triangular Systems | p. 106 |
| The LU Factorization | p. 111 |
| Round off Error in Gaussian Elimination | p. 122 |
| Pivoting | p. 125 |
| Improving and Estimating Accuracy | p. 137 |
| Parallel LU | p. 144 |
| Special Linear Systems | p. 153 |
| Diagonal Dominance and Symmetry | p. 154 |
| Positive Definite Systems | p. 159 |
| Banded Systems | p. 176 |
| Symmetric Indefinite Systems | p. 186 |
| Block Tridiagonal Systems | p. 196 |
| Vandermonde Systems | p. 203 |
| Classical Methods for Toeplitz Systems | p. 208 |
| Circulant and Discrete Poisson Systems | p. 219 |
| Orthogonalization and Least Squares | p. 233 |
| Householder and Givens Transformations | p. 234 |
| The QR Factorization | p. 246 |
| The Full-Rank Least Squares Problem | p. 260 |
| Other Orthogonal Factorizations | p. 274 |
| The Rank-Deficient Least Squares Problem | p. 288 |
| Square and Underdetermined Systems | p. 298 |
| Modified Least Squares Problems and Methods | p. 303 |
| Weighting and Regularization | p. 304 |
| Constrained Least Squares | p. 313 |
| Total Least Squares | p. 320 |
| Subspace Computations with the SVD | p. 327 |
| Updating Matrix Factorizations | p. 334 |
| Unsymmetric Eigenvalue Problems | p. 347 |
| Properties and Decompositions | p. 348 |
| Perturbation Theory | p. 357 |
| Power Iterations | p. 365 |
| The Hessenberg and Real Schur Forms | p. 376 |
| The Practical QR Algorithm | p. 385 |
| Invariant Subspace Computations | p. 394 |
| The Generalized Eigenvalue Problem | p. 405 |
| Hamiltonian and Product Eigenvalue Problems | p. 420 |
| Pseudospectra | p. 426 |
| Symmetric Eigenvalue Problems | p. 439 |
| Properties and Decompositions | p. 440 |
| Power Iterations | p. 450 |
| The Symmetric QR Algorithm | p. 458 |
| More Methods for Tridiagonal Problems | p. 467 |
| Jacobi Methods | p. 476 |
| Computing the SVD | p. 486 |
| Generalized Eigenvalue Problems with Symmetry | p. 497 |
| Functions of Matrices | p. 513 |
| Eigenvalue Methods | p. 514 |
| Approximation Methods | p. 522 |
| The Matrix Exponential | p. 530 |
| The Sign, Square Root, and Log of a Matrix | p. 536 |
| Large Sparse Eigenvalue Problems | p. 545 |
| The Symmetric Lanczos Process | p. 546 |
| Lanczos, Quadrature, and Approximation | p. 556 |
| Practical Lanczos Procedures | p. 562 |
| Large Sparse SVD Frameworks | p. 571 |
| Krylov Methods for Unsymmetric Problems | p. 579 |
| Jacobi-Davidson and Related Methods | p. 589 |
| Large Sparse Linear System Problems | p. 597 |
| Direct Methods | p. 598 |
| The Classical Iterations | p. 611 |
| The Conjugate Gradient Method | p. 625 |
| Other Krylov Methods | p. 639 |
| Preconditioning | p. 650 |
| The Multigrid Framework | p. 670 |
| Special Topics | p. 681 |
| Linear Systems with Displacement Structure | p. 681 |
| Structured-Rank Problems | p. 691 |
| Kronecker Product Computations | p. 707 |
| Tensor Unfoldings and Contractions | p. 719 |
| Tensor Decompositions and Iterations | p. 731 |
| Index | p. 747 |
| Table of Contents provided by Ingram. All Rights Reserved. |
