Title: A Parallel Dense-Matrix Eigensolver
 
Speaker: Mark Sears, SNL
                              
Date/Time: Thursday, October 20, 2005, 10:00-11:00 am

Location: Building 980, Room 95 (Sandia NM)

Brief Abstract: Good eigensolver technology has been around for some time,   for example reference implementations of several algorithms in   LAPACK are readily available. However, there has been a need   for a high performance parallel dense-matrix eigensolver for   the symmetric/Hermitian case especially in the electronic   structure community. High performance in the modern computing   environment means good parallel scaling in addition to using   the best possible BLAS implementation. This has been somewhat   difficult to achieve with currently available algorithms,   primarily because of the reduction to tridiagonal form. Many   people have suggested that reducing to a band form would be   more efficient, but then the problem of dealing with a banded   matrix is difficult to solve.

This talk will cover a new algorithm which I have developed   for the dense matrix Hermitian eigenproblem. This algorithm is   based on reduction to a band form rather than tridiagonal form, and this is coupled to a direct band eigensolver, which uses a combination of bisection and a new form of inverse iteration based on QR, both highly parallel. However, this is just the beginning. For a practical eigensolver a high performance parallel implementation using the best available BLAS is essential. In addition for the general case $Ax = \lambda Bx$ a number of other high performance parallel algorithms are needed, including matrix multiply, Cholesky factorization, and triangular solves. My implementation uses a block-cyclic decomposition for all of these algorithms. I will also present some impressive results for scaling and absolute performance.