Polynomial Acceleration for Restarted Arnoldi Iteration and its Parallelization

We propose an accelerating method for the restarted Arnoldi iteration to compute a number of eigenvalues of the standard eigenproblem Ax = x and discuss the dependence of the convergence rate of the accelerated iteration on the distribution of spectrum. The e ectiveness of the approach is proved by numerical results. We also propose a new parallelization technique for the nonsymmetric double shifted QR algorithm with perfect load balance and uninterrupted pipelining on distributed memory parallel architectures, which is strongly required from the viewpoint of complexity of the Arnoldi iteration. Its parallel e ciency is much higher than those reported in other papers.