By David S. Watkins
ISBN-10: 0898716411
ISBN-13: 9780898716412
This e-book provides the 1st in-depth, entire, and unified theoretical dialogue of the 2 most crucial periods of algorithms for fixing matrix eigenvalue difficulties: QR-like algorithms for dense difficulties and Krylov subspace equipment for sparse difficulties. the writer discusses the speculation of the general GR set of rules, together with specified instances (for instance, QR, SR, HR), and the improvement of Krylov subspace tools. additionally addressed are a established Krylov approach and the Arnoldi and diverse Lanczos algorithms, that are got as distinctive circumstances. The bankruptcy on product eigenvalue difficulties presents additional unification, exhibiting that the generalized eigenvalue challenge, the singular price decomposition challenge, and different product eigenvalue difficulties can all be seen as usual eigenvalue difficulties.
the writer offers theoretical and computational workouts during which the scholar is guided, step-by-step, to the implications. many of the workouts consult with a set of MATLAB® courses compiled through the writer which are to be had on an internet site that supplementations the publication.
Audience: Readers of this e-book are anticipated to be conversant in the fundamental rules of linear algebra and to have had a few event with matrix computations. This booklet is meant for graduate scholars in numerical linear algebra. it is going to even be worthwhile as a reference for researchers within the region and for clients of eigenvalue codes who search a greater realizing of the tools they're utilizing.
Contents: Preface; bankruptcy 1: initial fabric; bankruptcy 2: easy conception of Eigensystems; bankruptcy three: removal; bankruptcy four: new release; bankruptcy five: Convergence; bankruptcy 6: The Generalized Eigenvalue challenge; bankruptcy 7: contained in the Bulge; bankruptcy eight: Product Eigenvalue difficulties; bankruptcy nine: Krylov Subspace equipment; Bibliography; Index.
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The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods by David S. Watkins
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