Parallel Eigenvalue Routines on the Fujitsu VPP 300

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 rst 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 multisectioning algorithm to nd the eigenvalues and inverse iteration to nd the eigenvectors. The inverse iteration step achieves high performance because of a wrap-around partitioning algorithm for solving a tridi-agonal system.