Numerical methods for large eigenvalue problems / Youcef Saad

Saad, Youcef

ISBN 10: 0470218207 / ISBN 13: 9780470218204

Published by Manchester, UK New York : Manchester University Press ; Halsted Press, 1992

About this Item

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. 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 1 Kg.

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Bibliographic Details

• Title: Numerical methods for large eigenvalue problems / Youcef Saad
• Publisher: Manchester, UK New York : Manchester University Press ; Halsted Press
• Publication Date: 1992
• Language: English
• ISBN 10: 0470218207
• ISBN 13: 9780470218204
• Binding: Hardcover
• Edition: First Edition.

About this title

Synopsis

Offers a timely, in-depth perspective of numerical techniques used in solving large matrix eigenvalue problems arising in diverse engineering and scientific applications. Although important material for symmetric problems is covered, the focus is placed on more difficult nonsymmetric issues. Features solid theoretical treatment-- all of the latest plus well-known methods--and lists of some key computer programs.

Book Description

This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices. For researchers in applied mathematics and scientific computing, and can also be used as a supplementary text for an advanced graduate course on these methods.