Numerical methods for large eigenvalue problems / Youcef Saad
1992, First Edition. Manchester, UK New York : Manchester University Press ; Halsted Press. Near-fine copy in the original illustrated, paper-covered boards. Spine bands and panel edges slightly dulled and dust-toned as with age. Corners sharp with an overall tight, bright and clean impression. Item #385855
ISBN: 0470218207
Physical description; 346 pages : illustrations ; 24 cm. Notes: Includes bibliographical references (pages 323-340) and index.
Contents: 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 Techniques and Hybrid Methods. 1. The Basic Chebyshev Iteration. 2. Arnoldi-Chebyshev Iteration. 3. Deflated Arnoldi-Chebyshev. 4. Chebyshev Subspace Iteration. 5. Least Squares -- Arnoldi -- VIII. Preconditioning Techniques. 1. Shift-and-invert Preconditioning. 2. Polynomial Preconditioning. 3. Davidson's Method. 4. Generalized Arnoldi Algorithms -- IX. Non-Standard Eigenvalue Problems. 1. Introduction. 2. Generalized Eigenvalue Problems. 3. Quadratic Problems -- X. Origins of Matrix Eigenvalue Problems. 1. Introduction. 2. Mechanical Vibrations. 3. Electrical Networks. 4. Quantum Chemistry. 5. Stability of Dynamical Systems. 6. Bifurcation Analysis. 7. Chemical Reactions. 8. Macro-economics. 9. Markov Chain Models. Subjects: Nonsymmetric matrices.
Eigenvalues. Matrices asymétriques. Valeurs propres. Eigenvalues.
Nonsymmetric matrices.
Valeurs propres. Matrices.
Matrices.
Price: €125.00