Performance of the parallel block Jacobi method with dynamic ordering for the symmetric eigenvalue problem

Abstract

We investigate the performance of the parallel block Jacobi method for the symmetric eigenvalue problem with dynamic ordering both theoretically and experimentally. First, we present an improved global convergence theorem of the method that takes into account the effect of annihilating multiple blocks at once. Next, we compare the dynamic ordering with two representative parallel cyclic orderings experimentally and show that the former can speedup the convergence for ill-conditioned matrices considerably with little extra cost.