The matrix eigenvalue problem; GR and Krylov subspace methods

The matrix eigenvalue problem; GR and Krylov subspace methods.

Watkins, David S.

SIAM

2007

442 pages

$99.00

Paperback

Other titles in applied mathematics; 101

QA193

In this text for graduate students in numerical linear algebra, Watkins (mathematics, Washington State University) presents a 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. He discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, and HR). He also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. A chapter on product eigenvalue problems provides further unification, showing that the generalized eigenvalue problem, the singular value decomposition problem, and other product eigenvalue problems can all be viewed as standard eigenvalue problems. Theoretical and computational exercises are included, with some exercises referring to a collection of MATLAB programs available on a companion Web site. Readers should be familiar with basic ideas of linear algebra and matrix computations.

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