A parallel implementation of the eigenproblem for large, symmetric and sparse matrices

Abstract

This work studies the eigenproblem of large, sparse and sym- metric matrices through algorithms implemented in distributed memory multiprocessor architectures. The implemented parallel algorithm operates in three stages: structuring input matrix (Lanczos Method), computing eigenvalues (Sturm Sequence) and computing eigenvectors (Inverse Iteration). Parallel implementation has been carried out using a SPMD programming model and the PVM standard library. Algorithms have been tested in a multiprocessor system Cray T3E. Speed-up, load balance, cache faults and profile are discussed. From this study, it follows that for large input matrices our parallel implementations perceptibly improve the management of the memory hierarchy.