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I. Background In Matrix Theory And Linear Algebra. 1. Matrices. 2. Square Matrices And Eigenvalues. 3. Types Of Matrices. 4. Vector Inner Products And Norms. 5. Matrix Norms. 6. Subspaces. 7. Orthogonal Vectors And Subspaces. 8. Canonical Forms Of Matrices. 9. Normal And Hermitian Matrices. 10. Nonnegative Matrices -- Ii. Sparse Matrices. 1. Introduction. 2. Storage Schemes. 3. Basic Sparse Matrix Operations. 4. Sparse Direct Solution Methods. 5. Test Problems. 6. Sparskit -- Iii. Perturbation Theory And Error Analysis. 1. Projectors And Their Properties. 2. A-posteriori Error Bounds. 3. Conditioning Of Eigen-problems. 4. Localization Theorems -- Iv. The Tools Of Spectral Approximation. 1. Single Vector Iterations. 2. Deflation Techniques. 3. General Projection Methods. 4. Chebyshev Polynomials -- V. Subspace Iteration. 1. Simple Subspace Iteration. 2. Subspace Iteration With Projection. 3. Practical Implementations -- Vi. Krylov Subspace Methods. 1. Krylov Subspaces. 2. Arnoldi's Method. 3. The Hermitian Lanczos Algorithm. 4. Non-hermitian Lanczos Algorithm. 5. Block Krylov Methods. 6. Convergence Of The Lanczos Process. 7. Convergence Of The Arnoldi Process -- Vii. Acceleration T

Author

Youcef Saad

Publisher

New York, N.Y. : New York, N.Y. : Manchester University Press, J. Wiley and Sons. Halsted Press

Published

1992

Language

EN

ISBN

9780470218204

Subjects

Mathematics, Stem