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| Preface | |
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| Acknowledgments | |
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| Gaussian Elimination and Its Variants | |
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| Matrix Multiplication | |
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| Systems of Linear Equations | |
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| Triangular Systems | |
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| Positive Definite Systems; Cholesky Decomposition | |
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| Banded Positive Definite Systems | |
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| Sparse Positive Definite Systems | |
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| Gaussian Elimination and the LU Decomposition | |
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| Gaussian Elimination with Pivoting | |
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| Sparse Gaussian Elimination | |
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| Sensitivity of Linear Systems | |
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| Vector and Matrix Norms | |
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| Condition Numbers | |
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| Perturbing the Coefficient Matrix | |
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| A Posteriori Error Analysis Using the Residual | |
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| Roundoff Errors; Backward Stability | |
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| Propagation of Roundoff Errors | |
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| Backward Error Analysis of Gaussian Elimination | |
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| Scaling | |
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| Componentwise Sensitivity Analysis | |
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| The Least Squares Problem | |
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| The Discrete Least Squares Problem | |
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| Orthogonal Matrices, Rotators, and Reflectors | |
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| Solution of the Least Squares Problem | |
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| The Gram-Schmidt Process | |
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| Geometric Approach | |
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| Updating the QR Decomposition | |
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| The Singular Value Decomposition | |
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| Introduction | |
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| Some Basic Applications of Singular Values | |
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| The SVD and the Least Squares Problem | |
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| Sensitivity of the Least Squares Problem | |
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| Eigenvalues and Eigenvectors I | |
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| Systems of Differential Equations | |
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| Basic Facts | |
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| The Power Method and Some Simple Extensions | |
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| Similarity Transforms | |
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| Reduction to Hessenberg and Tridiagonal Forms | |
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| Francis's Algorithm | |
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| Use of Francis's Algorithm to Calculate Eigenvectors | |
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| The SVD Revisited | |
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| Eigenvalues and Eigenvectors II | |
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| Eigenspaces and Invariant Subspaces | |
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| Subspace Iteration and Simultaneous Iteration | |
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| Krylov Subspaces and Francis's Algorithm | |
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| Large Sparse Eigenvalue Problems | |
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| Implicit Restarts | |
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| The Jacobi-Davidson and Related Algorithms | |
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| Eigenvalues and Eigenvectors III | |
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| Sensitivity of Eigenvalues and Eigenvectors | |
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| Methods for the Symmetric Eigenvalue Problem | |
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| Product Eigenvalue Problems | |
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| The Generalized Eigenvalue Problem | |
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| Iterative Methods for Linear Systems | |
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| A Model Problem | |
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| The Classical Iterative Methods | |
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| Convergence of Iterative Methods | |
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| Descent Methods; Steepest Descent | |
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| On Stopping Criteria | |
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| Preconditioners | |
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| The Conjugate-Gradient Method | |
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| Derivation of the CG Algorithm | |
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| Convergence of the CG Algorithm | |
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| Indefinite and Nonsymmetric Problems | |
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| References | |
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| Index | |
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| Index of MATLAB� Terms | |