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| Preface | |
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| Global References | |
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| Other Books | |
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| Useful URLs | |
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| Common Notation | |
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| Matrix Multiplication | |
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| Basic Algorithms and Notation | |
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| Structure and Efficiency | |
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| Block Matrices and Algorithms | |
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| Fast Matrix-Vector Products | |
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| Vectorization and Locality | |
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| Parallel Matrix Multiplication | |
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| Matrix Analysis | |
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| Basic Ideas from Linear Algebra | |
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| Vector Norms | |
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| Matrix Norms | |
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| The Singular Value Decomposition | |
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| Subspace Metrics | |
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| The Sensitivity of Square Systems | |
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| Finite Precision Matrix Computations | |
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| General Linear Systems | |
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| Triangular Systems | |
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| The LU Factorization | |
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| Round off Error in Gaussian Elimination | |
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| Pivoting | |
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| Improving and Estimating Accuracy | |
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| Parallel LU | |
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| Special Linear Systems | |
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| Diagonal Dominance and Symmetry | |
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| Positive Definite Systems | |
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| Banded Systems | |
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| Symmetric Indefinite Systems | |
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| Block Tridiagonal Systems | |
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| Vandermonde Systems | |
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| Classical Methods for Toeplitz Systems | |
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| Circulant and Discrete Poisson Systems | |
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| Orthogonalization and Least Squares | |
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| Householder and Givens Transformations | |
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| The QR Factorization | |
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| The Full-Rank Least Squares Problem | |
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| Other Orthogonal Factorizations | |
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| The Rank-Deficient Least Squares Problem | |
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| Square and Underdetermined Systems | |
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| Modified Least Squares Problems and Methods | |
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| Weighting and Regularization | |
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| Constrained Least Squares | |
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| Total Least Squares | |
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| Subspace Computations with the SVD | |
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| Updating Matrix Factorizations | |
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| Unsymmetric Eigenvalue Problems | |
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| Properties and Decompositions | |
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| Perturbation Theory | |
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| Power Iterations | |
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| The Hessenberg and Real Schur Forms | |
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| The Practical QR Algorithm | |
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| Invariant Subspace Computations | |
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| The Generalized Eigenvalue Problem | |
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| Hamiltonian and Product Eigenvalue Problems | |
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| Pseudospectra | |
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| Symmetric Eigenvalue Problems | |
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| Properties and Decompositions | |
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| Power Iterations | |
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| The Symmetric QR Algorithm | |
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| More Methods for Tridiagonal Problems | |
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| Jacobi Methods | |
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| Computing the SVD | |
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| Generalized Eigenvalue Problems with Symmetry | |
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| Functions of Matrices | |
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| Eigenvalue Methods | |
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| Approximation Methods | |
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| The Matrix Exponential | |
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| The Sign, Square Root, and Log of a Matrix | |
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| Large Sparse Eigenvalue Problems | |
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| The Symmetric Lanczos Process | |
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| Lanczos, Quadrature, and Approximation | |
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| Practical Lanczos Procedures | |
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| Large Sparse SVD Frameworks | |
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| Krylov Methods for Unsymmetric Problems | |
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| Jacobi-Davidson and Related Methods | |
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| Large Sparse Linear System Problems | |
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| Direct Methods | |
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| The Classical Iterations | |
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| The Conjugate Gradient Method | |
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| Other Krylov Methods | |
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| Preconditioning | |
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| The Multigrid Framework | |
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| Special Topics | |
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| Linear Systems with Displacement Structure | |
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| Structured-Rank Problems | |
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| Kronecker Product Computations | |
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| Tensor Unfoldings and Contractions | |
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| Tensor Decompositions and Iterations | |
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| Index | |