The Spectral Decomposition of Nonsymmetric Matrices on Distributed Memory Parallel Computers

The implementation and performance of a class of divide-and-conquer algorithms for computing the spectral decomposition of nonsymmetric matrices on distributed memory parallel computers are studied in this paper. After presenting a general framework, we focus on a spectral divide-and-conquer (SDC) algorithm with Newton iteration. Although the algorithm requires several times as many floating point operations as the best serial QR algorithm, it can be simply constructed from a small set of highly parallelizable matrix building blocks within Level 3 BLAS. Efficient implementations of these building blocks are available on a wide range of machines. In some ill-conditioned cases, the algorithm may lose numerical stability, but this can easily be detected and compensated for. The algorithm reached 31% efficiency with respect to the underlying PUMMA matrix multiplication and 82% efficiency with respect to the underlying ScaLAPACK matrix inversion on a 256 processor Intel Touchstone Delta sys..