Templates for the solution of algebraic eigenvalue problems. A practical guide. (English) Zbl 0965.65058

Software - Environments - Tools. 11. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xxix, 410 p. (2000).
The book is edited and written by well-known names in the field and is an excellent guide to the numerical solution of eigenvalue problems. It presents the many available methods in an organized fashion.
Chapter 1 is introductory. Chapter 2 provides the top level of a decision tree for classifying eigenvalue problems and their corresponding numerical methods. Chapter 3 summarizes the two mathematical principles used by most algorithms for large eigenvalue problems: projection onto subspaces and spectral transformations.
Chapters 4 through 9 give details for each of the six categories of eigenvalue problems: Hermitian, generalized Hermitian, non-Hermitian, generalized non-Hermitian, and nonlinear eigenvalue problems, and the singular value decomposition. The descriptions include algorithm templates and pointers to available software. Chapter 10 describes common isues of sparse matrix representation and computation, both sequentially and in parallel, shared by all algorithms. Chapter 11 describes some preconditioning techniques that are subject of current research.
The subjects not covered by the book are referenced for the interested reader.


65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices
65Y05 Parallel numerical computation
00B15 Collections of articles of miscellaneous specific interest
65-06 Proceedings, conferences, collections, etc. pertaining to numerical analysis
65F35 Numerical computation of matrix norms, conditioning, scaling
65F20 Numerical solutions to overdetermined systems, pseudoinverses
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