The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods

The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods

By: David S. Watkins (author)Paperback

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Description

The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.

About Author

David S. Watkins is professor of mathematics at Washington State University.

Contents

Preface; 1. Preliminary material; 2. Basic theory of Eigensystems; 3. Elimination; 4. Iteration; 5. Convergence; 6. The generalized Eigenvalue problem; 7. Inside the bulge; 8. Product Eigenvalue problems; 9. Krylov subspace methods; Bibliography; Index.

Product Details

  • ISBN13: 9780898716412
  • Format: Paperback
  • Number Of Pages: 456
  • ID: 9780898716412
  • weight: 756
  • ISBN10: 0898716411

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