| Description |
1 online resource (xiv, 258 pages) : illustrations |
| Series |
Lecture notes in computational science and engineering, 1439-7358 ; 46 |
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Lecture notes in computational science and engineering ; 46. 1439-7358
|
| Contents |
Cover -- Preface -- Table of Contents -- 1 The QR Algorithm -- 1.1 The Standard Eigenvalue Problem -- 1.2 Perturbation Analysis -- 1.3 The Basic QR Algorithm -- 1.4 Balancing -- 1.5 Block Algorithms -- 1.6 Advanced Deflation Techniques -- 1.7 Computation of Invariant Subspaces -- 1.8 Case Study: Solution of an Optimal Control Problem -- 2 The QZ Algorithm. -- 2.1 The Generalized Eigenvalue Problem. -- 2.2 Perturbation Analysis -- 2.3 The Basic QZ Algorithm -- 2.4 Balancing -- 2.5 Block Algorithms -- 2.6 Aggressive Early Deflation -- 2.7 Computation of Deflating Subspaces -- 3 The Krylov-Schur Algorithm -- 3.1 Basic Tools -- 3.2 Restarting and the Krylov-Schur Algorithm -- 3.3 Balancing Sparse Matrices -- 4 Structured Eigenvalue Problems -- 4.1 General Concepts. -- 4.2 Products of Matrices -- 4.3 Skew-Hamiltonian and Hamiltonian Matrices -- 4.4 Skew-Hamiltonian Matrices -- 4.5 Hamiltonian matrices -- 4.6 A Bouquet of Other Structures -- A Background in Control Theory -- B Software -- References |
| Summary |
This book is about computing eigenvalues, eigenvectors and invariant subspaces of matrices. The treatment includes generalized and structured eigenvalue problems, such as Hamiltonian or product eigenvalue problems. All vital aspects of eigenvalue computations are covered: theory, perturbation analysis, algorithms, high performance methodologies and software. The reader will learn about recently developed techniques which substantially improve the performance of some of the most widely numerical methods, the QR and the QZ algorithm as well as Krylov subspace methods. A unique feature of this bo |
| Bibliography |
Includes bibliographical references (pages 233-251) and index |
| Notes |
English |
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Print version record |
| In |
Springer e-books |
| Subject |
Eigenvalues.
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Structural analysis (Engineering) -- Matrix methods.
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MATHEMATICS -- Algebra -- Elementary.
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Structural analysis (Engineering) -- Matrix methods.
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Eigenvalues.
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Autovalores
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Eigenvalues
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Structural analysis (Engineering) -- Matrix methods
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| Form |
Electronic book
|
| ISBN |
9783540285021 |
|
3540285024 |
|
3540245464 |
|
9783540245469 |
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6610337373 |
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9786610337378 |
|
1280337370 |
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9781280337376 |
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