A parallel iterative method for solving symmetric tridiagonal extreme eigenpair problems

AbstractIn this paper, we propose a parallel iterative method for calculating the extreme eigenpair (the largest or smallest eigenvalue and corresponding eigenvector) of a large symmetric tridiagonal matrix. It is based upon a divide and repeated, rank-one modification technique. The rank-one modification with a parameter only changes one diagonal element of each submatrix. We present a basic theory for subdividing the extremal eigenpair problem and then prove several convergence theorems that show the convergence of the iteration scheme for any positive initial modification parameter and the asymptotical quadratic convergence rate. Some numerical experiments are given, which show the efficiency of the parallel algorithm