This classic textbook provides a unified treatment of spectral approximation for closed or bounded operators as well as for matrices. Despite significant changes and advances in the field since it was first published in 1983, the book continues to form the theoretical bedrock for any computational approach to spectral theory over matrices or linear operators. This coverage of classical results is not readily available elsewhere.
Spectral Approximation of Linear Operators offers in-depth coverage of properties of various types of operator convergence, the spectral approximation of non–self-adjoint operators, a generalization of classical perturbation theory, and computable errors bounds and iterative refinement techniques, along with many exercises (with solutions), making it a valuable textbook for graduate students and reference manual for self-study.
This book is appropriate for advanced undergraduate students and graduate students, researchers in functional and/or numerical analysis, and engineers who work on instability and turbulence.
Preface to the Classics Edition;
List of Errata;
Chapter 1: The Matrix Eigenvalue Problem;
Chapter 2: Elements of Functional Analysis: Basic Concepts;
Chapter 3: Elements of Functional Analysis: Convergence and Perturbation Theory;
Chapter 4: Numerical Approximation Methods for Integral and Differential Operators;
Chapter 5: Spectral Approximation of a Closed Linear Operator;
Chapter 6: Error Bounds and Localization Results for the Eigenelements;
Chapter 7: Some Examples of Applications;
Appendix: Discrete Approximation Theory;
Solutions to Exercises;
About the Author
Françoise Chatelin is Professor of Mathematics at the University of Toulouse and head of the Qualitative Computing Group at CERFACS. Her areas of expertise include spectral theory for linear operators in Banach spaces and finite precision computation of very large eigenproblems.
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spectral theory, closed operators, isolated eigenvalues, strongly stable approximation, a posteriori error bounds
2011 / xxvii + 458 / Softcover / ISBN 978-0-898719-99-4
List Price $75.00 / SIAM Member Price $52.50/ Order Code CL65