An improved subspace iteration method with shifting

An efficient and stable technique to remove the limitation in choosing a sh ift in the subspace iteration method with shifting is presented. A major di fficulty of the subspace iteration method with shifting is that, because of the singularity problem, a shift close to an eigenvalue cannot be used, re sulting in slower convergence. This study solves the above singularity prob lem using side conditions without sacrifice of convergence. The method is a lways nonsingular even if a shift is an eigenvalue itself This is one of th e significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least eq ual to that of the subspace iteration method with shifting, and the operati on counts of above two methods are almost the same for large structures. To show the effectiveness of the proposed method, two numerical examples are considered. (C) 1999 Elsevier Science Ltd. Ail rights reserved.