A REFINED ITERATIVE ALGORITHM-BASED ON THE BLOCK ARNOLDI PROCESS FOR LARGE UNSYMMETRIC EIGENPROBLEMS

When the matrix in question is unsymmetric, the approximate eigenvecto rs or Ritz vectors obtained by orthogonal projection methods including Arnoldi's method and the block Arnoldi method cannot be guaranteed to converge in theory even if the corresponding approximate eigenvalues or Ritz values do. In order to circumvent this danger, a new strategy has been proposed by the author for Arnoldi's method. The strategy use d is generalized to the block Arnoldi method in this paper. It discard s Ritz vectors and instead computes refined approximate eigenvectors b y small-sized singular-value decompositions. It is proved that the new strategy can guarantee the convergence of refined approximate eigenve ctors if the corresponding Ritz values do. The resulting refined itera tive algorithm is realized by the block Arnoldi process. Numerical exp eriments show that the refined algorithm is much more efficient than t he iterative block Arnoldi algorithm. (C) 1998 Elsevier Science Inc.