Françoise Chatelin
Classics in Applied Mathematics 71
This classic textbook provides a modern and complete guide to the calculation of eigenvalues of matrices, written at an accessible level that presents in matrix notation the fundamental aspects of the spectral theory of linear operators in finite dimension. Unique features of Eigenvalues of Matrices, Revised Edition are • the convergence of eigensolvers serving as the basis of the notion of the gap between invariant subspaces, • its coverage of the impact of the high nonnormality of the matrix on its eigenvalues, and • the comprehensive nature of the material that moves beyond mathematical technicalities to the essential mean carried out by matrix eigenvalues.
Audience The book’s primary use is as a course text for undergraduate students in mathematics, applied mathematics, physics, and engineering. It is also useful as a reference for researchers or for engineers in hightech industries who are confronted with instability and chaos in intensive computing that results from the strong coupling of two distinct phenomena.
About the Author Françoise Chatelin is Professor of Mathematics at the University of Toulouse and head of the Qualitative Computing Group at CERFACS. Before moving to CERFACS, she was a professor at the universities of Grenoble and Paris IX Dauphine. She also worked for a decade in the industrial research laboratories of IBM France and Thales, where she was in charge of intensive computing activities. Her areas of expertise include spectral theory for linear operators in Banach spaces and finite precision computation of very large eigenproblems. She currently explores the uncharted domain of mathematical computation that lies beyond real or complex analysis.
Contents Preface to the Classics Edition; Preface; Preface to the English Edition; Notation; List of Errata; Chapter 1: Supplements from Linear Algebra; Chapter 2: Elements of Spectral Theory; Chapter 3: Why Compute Eigenvalues?; Chapter 4: Error Analysis; Chapter 5: Foundations of Methods for Computing Eigenvalues; Chapter 6: Numerical Methods for Large Matrices; Chapter 7: Chebyshev’s Iterative Methods; Chapter 8: Polymorphic Information Processing with Matrices; Appendix A: Solution to Exercises; Appendix B: References for Exercises; Appendix C: References; Index.
To request an examination copy or desk copy of this book, please use our online request form at www.siam.org/catalog/adopt.php.
Keywords eigenvalue, matrix, Cauchy integral, spectral conditioning, gap between invariant subspaces
2012 / xxx + 410 pages / Softcover / ISBN 9781611972450 List Price $99.00 / SIAM Member Price $69.30 / Order Code CL71
