Numerical methods for large eigenvalue problems. Revised ed. (English) Zbl 1242.65068

Saad, Yousef

Classics in Applied Mathematics 66. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611970-72-2/pbk; 978-1-611970-73-9/ebook). xvi, 276 p. (2011).

All chapters in this revised edition of Y. Saad’s important book [Algorithms and Architectures for Advanced Scientific Computing. Manchester: Manchester University Press. New York, NY: Halsted Press (1992; Zbl 0991.65039)] have undergone some revision, but it is the chapters dealing with the rapidly evolving topics of algorithms and their implementation that are changed the most. In the first six chapters, the revision is relatively minor, but with new sections on sparse matrix repositories and MATLAB in chapter 2 and on pseudo-eigenvalues in chapter 3. However, chapter 7 is largely rewritten with a new title, filtering and restarting techniques. Chapter 8 (preconditioning techniques) is also substantially revised. In chapter 10 on applications, the old section on quantum chemistry is greatly expanded and now has the title, electronic structure calculations. There are now 229 references, with the new additions mostly recent, and the “notes and references” sections at the end of each chapter have also been revised.

Reviewer: Alan L. Andrew (Bundoora)

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis
65F50	Computational methods for sparse matrices
65F08	Preconditioners for iterative methods
65F10	Iterative numerical methods for linear systems

Keywords:

matrix eigenvalue problems; Krylov subspace methods; perturbation theory; large sparse non-Hermitian matrices; spectral approximation; preconditioning; convergence acceleration; pseudo-eigenvalues; filtering; restarting; quantum chemistry; electronic structure calculations

Software:

ARPACK; BLAS; Eigtool; EISPACK; JADAMILU; JDQR; JDQZ; LAPACK; LINPACK; Matlab; SRRIT