Matrix computations. 2nd ed. (English) Zbl 0733.65016

Golub, Gene H.; Van Loan, Charles F.

Johns Hopkins Series in the Mathematical Sciences, 3. Baltimore etc.: The Johns Hopkins University Press. xix, 642 p. $ 68.50/hbk; $ 34.50/pbk (1989).

This is a considerable update and expansion of a text (first edition 1983; Zbl 0559.65011) that has already become a standard reference in the linear algebra community. Two new chapters, on matrix multiplication and parallel matrix computation, give an introduction to this very technical and still fluid subject area. Very detailed algorithms given in a notation very close to MATLAB are given for most of the methods studied. Each chapter contains current and relevant references to the original works, making this an excellent handbook for the researcher and practitioner.

Reviewer: A.Ruhe (Göteborg)

MSC:

65Fxx	Numerical linear algebra
65Y05	Parallel numerical computation
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
15A18	Eigenvalues, singular values, and eigenvectors
15A60	Norms of matrices, numerical range, applications of functional analysis to matrix theory

Keywords:

matrix computations; matrix algebra; Gaussian elimination; orthogonalization; least squares methods; eigenvalue problem; Lanczos methods; iterative methods; functions of matrices; matrix multiplication; parallel matrix computation; MATLAB

Software:

Matlab