The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods

Watkins, David S.

ISBN 10: 0898716411 / ISBN 13: 9780898716412

Editore: Society for Industrial and Applied Mathematics, 2008

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Titolo: The Matrix Eigenvalue Problem: GR and Krylov...

Casa editrice: Society for Industrial and Applied Mathematics

Data di pubblicazione: 2008

Legatura: Brossura

Condizione: Good

Descrizione articolo

Riassunto:

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.

Recensione:

'This is an excellent exposition of the state of the art in eigenvalue computations. It systematically combines the theory and the computational methods for structured and unstructured problems in a unique framework.' Volker Mehrmann, Technische Universität Berlin