Parallel eigenvalue routines on the Fujitsu VPP300

Research Report MRR97-054

Parallel eigenvalue routines on the Fujitsu VPP300

David L. Harrar II, Margaret H. Kahn, Michael R. Osborne

Abstract: As part of the Fujitsu-ANU Parallel Mathematical Subroutine Library Project we have developed a suite of parallel eigenvalue decomposition routines to handle a variety of input matrices. For a dense real symmetric matrix there are routines using the Jacobi algorithm and routines which first reduce the symmetric matrix to tridiagonal form. All algorithms have been developed to fully exploit the vector capabilities of the VPP300. Many approaches require the eigendecomposition of a tridiagonal matrix and high performance for this step has been obtained by using a multisection algorithm to find the eigenvalues and inverse iteration to compute the eigenvectors. The inverse iteration step achieves high performance through the use of a wrap-around partitioning algorithm for solving tridiagonal systems.

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