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.
Sprache
Verlagsort
Verlagsgruppe
Cambridge University Press
Zielgruppe
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. This book is intended for graduate students in numerical linear algebra. It will also be useful as a reference for researchers in the area and for users of eigenvalue codes who seek a better understanding of the methods they are using.
Maße
Höhe: 254 mm
Breite: 174 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-89871-641-2 (9780898716412)
Schweitzer Klassifikation
Autor*in
Washington State University
David S. Watkins is professor of mathematics at Washington State University.
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.
