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Linear Algebra problems appear ubiquitously in many applications (formulations) across computational science and engineering. We have been undertaking a broad range of synergistic activities in designing and implementing numerical linear algebra algorithms. We target a range of dense and sparse linear systems and eigenvalue problems. Our overall goal is to produce the fastest and most accurate solvers for these problems, make them available to a broad and changing user community, and meet the opportunities and challenges of new architectures in growing use.

In this talk, we shall present an overview of these activities and then focus on algorithm design and development of traditional ``black-box'' software, such as LAPACK, and emerging ``template'' software for solving linear algebra problems.

This is a joint work with Jim Demmel at UC Berkeley and Jack Dongarra at UT Knoxville and Oak Ridge National Labs.