A parallel implementation of the symmetric tridiagonal QR algorithm

Abstract

The authors propose a novel and simple way to parallelize the QR algorithm for computing eigenvalues and eigenvectors of real symmetric tridiagonal matrices. This approach is suitable for all parallel computers, ranging from multiprocessor supercomputers with shared memory to massively parallel computers with local memory. The authors report on numerical experiments completed on a Cray-Y-MP, an Alliant FX-80, a Sequent Symmetry S81b, a nCUBE 2, a Thinking Machines CM200, and a cluster of Sun SPARCstations. The numerical results indicate that the proposed algorithm is suitable for parallel execution on the whole range of parallel computers. While the results obtained on the computers with vector facilities did not show very high efficiencies, those obtained with multiprocessor computers with scalar CPUs had very good speedups. >