Performance Evaluation of Some Inverse Iteration Algorithms on PowerXCell 8i Processor

In this paper, we compare with the inverse iteration algorithms on PowerXCell 8i processor, which has been known as a heterogeneous environment. When some of all the eigenvalues are close together or there are clusters of eigenvalues, reorthogonalization must be adopted to all the eigenvectors associated with such eigenvalues. Reorthogonalization algorithms need a lot of computational cost. The Classical Gram-Schmidt (CGS) algorithm, the modified Gram-Schmidt (MGS) algorithm, and the Householder orthogonalization algorithm in terms of the compact WY representation have been known as reorthogonalization algorithms. These algorithms can be computed using BLAS level-1 and level-2. Since synergistic processor elements in PowerXCell 8i processor archive the high performance of BLAS level-2 and level-3, the orthogonalization algorithms except the MGS algorithm can be computed high-speed on parallel computers.