On parallelizing the MRRR algorithm for data-parallel coprocessors

Abstract

The eigenvalues and eigenvectors of a symmetric matrix are of interest in a myriad of applications. One of the fastest and most accurate numerical techniques for the eigendecomposition is the Algorithm of Multiple Relatively Robust Representations (MRRR), the first stable algorithm that computes the eigenvalues and eigenvectors of a tridiagonal symmetric matrix in O(n 2) arithmetic operations. In this paper we present a parallelization of the MRRR algorithm for data parallel coprocessors using the CUDA programming environment. The results demonstrate the potential of data-parallel coprocessors for scientific computations: compared to routine sstemr, LAPACK's implementation of MRRR, our parallel algorithm provides 10-fold speedups. © 2010 Springer-Verlag Berlin Heidelberg.