Exploiting the symmetry on the Jacobi method on a mesh of processors

We study the parallelization of the Jacobi method to solve the symmetric eigenvalue problem on a mesh of processors. To solve this problem obtaining a theoretical efficiency of 100% it is necessary to exploit the symmetry of the matrix. The only previous algorithm we know exploiting the symmetry on multicomputers uses a storage scheme adequate for a logical ring of processors, so having a low scalability. In this paper we show how matrix symmetry can be exploited on a logical mesh of processors obtaining a higher scalability than that obtained with the previous algorithm. In addition, we show how the storage scheme exploiting the symmetry can be combined with a scheme by blocks to obtain a highly efficient and scalable Jacobi method for solving the symmetric eigenvalue problem for distributed memory parallel computers. We report performance results from the Intel Touchstone DELTA