SIAM, 2012. — 429 p. — ISBN: 9781611972450This revised edition of a classic textbook provides a complete guide to the calculation of eigenvalues of matrices. Written at an accessible level, this modern exposition of the subject presents fundamental aspects of the spectral theory of linear operators in finite dimension. Unique features of this book include a treatment of the convergence of eigensolvers based on the notion of the gap between invariant subspaces, and coverage of the impact of the high nonnormality of a matrix on its eigenvalues. Also included is a new chapter uncovering reasons why matrices are fundamental tools for the information processing that takes place in the dynamical evolution of systems. Some of these ideas appear in print for the first time. The book's primary use is as a course text for undergraduate students in mathematics, applied mathematics, physics, and engineering. It is also a useful reference for researchers and engineers in industry.Contents
Preface to the classics edition
Preface
Preface to the English edition
Notation
List of errata
Supplements from linear algebra
Elements of spectral theory
Why compute eigenvalues?
Error analysis
Foundations of methods for computing eigenvalues
Numerical methods for large matrices
Chebyshev's iterative methods
Polymorphic information processing with matrices
Appendix. Solution to exercises
Appendix. References for exercises
References
Index.
