Numerical methods for large eigenvalue problems. (English) Zbl 0991.65039

Saad, Youcef

Algorithms and Architectures for Advanced Scientific Computing. Manchester: Manchester University Press. New York, NY: Halsted Press. vii, 346 p. (1992).

Ten years after its publication, this book remains an essential reference on the numerical solution of eigenvalue problems for large sparse non-Hermitian matrices. It also includes much important material for special cases, such as Hermitian matrices, and for the more general problem \(Ax=\lambda Bx\). Krylov subspace methods are emphasized, and a valuable guide to acceleration techniques is included. In spite of the rapid rate of developments in the field of numerical solution of large sparse eigenproblems, this book is likely to remain important for many years to come, in part because of the careful attention it gives to the theory underlying the numerical methods discussed, including proofs of the main results.

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
65F35	Numerical computation of matrix norms, conditioning, scaling

Keywords:

matrix eigenvalue problems; Krylov subspace methods; perturbation theory; spectral approximation; preconditioning; textbook; convergence acceleration; large sparse non-Hermitian matrices