LAPACK: A Portable Linear Algebra Library for High-Performance Computers

Abstract

The goal of the LAPACK project is to des i gn andimplementaportabl e l i near al gebralibrary for effici entuseonavariety of high-performance computers. The library is based on thewidel y used LINPACKandEISPACKpackages f or sol ving linear equat i ons , ei genval ueproblems, andlinear l east-squares problems, butextendsthei r f uncti onalityinanumber of ways. Themaj or methodol ogy f or makingthe al gor i thmsrun f aster is to restructure themto performblockmatr i x operat i ons (e. g. , matr i x-matr i x multiplication)inthei r i nner l oops. These block operat i onsmay beoptimi zed to exploit thememory hierarchy of a speci fic archi tecture. TheLAPACKproject i s al so working on new divide-and-conquer al gor i thms f or certai n ei genproblems, andnew al gor i thmsthat yieldhigher rel ati ve accuracy for avarietyof linear al gebra problems. 1 Introducti on TheUnivers i ty of Tennessee, theCourantInstitute for Mathemat i cal Sci ences, theNumer i cal Al gor i thmsGroupLtd., Rice Unive...