Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A. Numerical linear algebra for high-performance computers. (English) Zbl 0914.65014 Software - Environments - Tools. 7. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xviii, 342 p. (1998). This book presents techniques for solving matrix problems on parallel and vector computers. It begins with an overview of computer architecture as of 1998 and the issues involved in minimizing overhead and evaluating performance. Then it presents techniques for direct solution of dense matrix problems and least squares problems, algorithms for direct solution of sparse linear systems, preconditioned Krylov subspace methods for iterative solution, and Lanczos, Arnoldi, Davidson, and Jacobi-Davidson methods for eigenvalue and generalized eigenvalue problems. Available software packages (e.g., BLAS, LAPACK, ScaLAPACK, JDQR, ARPACK) are surveyed. Reviewer: W.Gander (Zürich) Cited in 1 ReviewCited in 75 Documents MSC: 65Fxx Numerical linear algebra 65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis 65Y10 Numerical algorithms for specific classes of architectures 65Y05 Parallel numerical computation 65Y15 Packaged methods for numerical algorithms Keywords:parallel computation; computer architecture; direct and iterative methods for linear systems; eigenvalue computations; textbook; Lanczos method; Arnoldi method; vector computers; least squares problems; algorithms; sparse linear systems; preconditioned Krylov subspace method; Jacobi-Davidson method; software packages; BLAS; LAPACK; ScaLAPACK; JDQR; ARPACK Software:ARPACK; JDQR; ScaLAPACK; LAPACK; MA47; LSQR; MA32; na5; DRIC; MA42 PDFBibTeX XMLCite \textit{J. J. Dongarra} et al., Numerical linear algebra for high-performance computers. Philadelphia, PA: SIAM (1998; Zbl 0914.65014) Full Text: DOI