The PRISM project: infrastructure and algorithms for parallel eigensolvers

The goal of the PRISM project is the development of infrastructure and algorithms for the parallel solution of eigenvalue problems. We are currently investigating a complete eigensolver based on the invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA). After briefly reviewing the SYISDA approach, we discuss the algorithmic highlights of a distributed-memory implementation of an eigensolver based on this approach. These include a fast matrix-matrix multiplication algorithm, a new approach to parallel band reduction and tridiagonalization, and a harness for coordinating the divide-and-conquer parallelism in the problem. We also present performance results of these kernels as well as the overall SYISDA implementation on the Intel Touchstone Delta prototype and the IBM SP/1