Hybrid algorithms for the elgensolution of large sparse symmetric matrices on the AMT DAP 510

Abstract

In this paper a method for the eigensolution of large sparse symmetric matrices with regular structures is presented. The method is applied by first extracting the diagonal submatrices of the target matrix and assembling from the matrices of their eigenvectors an approximation to the matrix of eigenvectors of the large system. The eigensolutions of the small matrices may be computed using any appropriate algorithm; indeed, the choice of algorithm may vary from submatrix to submatrix. The eigenvectors of the target system are then constructed by refining the matrix of approximate eigenvectors. The algorithm used in this refinement process may be efficiently implemented, for matrices of any size, on an array processor. In this paper experience of using the method on an AMT DAP 510 is reported, and the efficiency of its performance is favourably compared with a related method [1] for solving problems of a similar kind.