On Implementation and Evaluation of Inverse Iteration Algorithm with Compact WY Orthogonalization

Abstract

In this paper, we introduce an inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel processors. To overcome the sequential bottleneck created by modified Gram-Schmidt orthogonalization in classical inverse iteration, we propose the use of the compact WY representation in the reorthogonalization process, based on the Householder transformation. This change results in drastically reduced synchronization cost during parallel processing.