Spectral Computations for Bounded Operators

Mario Ahues, Alain Largillier, Balmohan Limaye

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English

Chapman & Hall/CRC
02 December 2019

Functional analysis & transforms; Algorithms & data structures; Maths for computer scientists

Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for research scientists, Spectral Computations for Bounded Operators addresses the issue of solving eigenvalue problems for operators on infinite dimensional spaces.

From a review of classical spectral theory through concrete approximation techniques to finite dimensional situations that can be implemented on a computer, this volume illustrates the marriage of pure and applied mathematics. It contains a variety of recent developments, including a new type of approximation that encompasses a variety of approximation methods but is simple to verify in practice. It also suggests a new stopping criterion for the QR Method and outlines advances in both the iterative refinement and acceleration techniques for improving the accuracy of approximations. The authors illustrate all definitions and results with elementary examples and include numerous exercises.

Spectral Computations for Bounded Operators thus serves as both an outstanding text for second-year graduate students and as a source of current results for research scientists.

By: Mario Ahues, Alain Largillier, Balmohan Limaye
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9780367455354
ISBN 10: 0367455358
Pages: 400
Publication Date: 02 December 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Ahues, Mario; Largillier, Alain; Limaye, Balmohan