An improved subspace iteration method with shifting

✍ Scribed by Hyung-Jo Jung; Man-Cheol Kim; In-Won Lee

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 292 KB
• Volume: 70
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(98)00201-6

✦ Synopsis

An ecient and stable technique to remove the limitation in choosing a shift in the subspace iteration method with shifting is presented. A major diculty of the subspace iteration method with shifting is that, because of the singularity problem, a shift close to an eigenvalue cannot be used, resulting in slower convergence. This study solves the above singularity problem using side conditions without sacri®ce of convergence. The method is always nonsingular even if a shift is an eigenvalue itself. This is one of the signi®cant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shifting, and the operation counts of above two methods are almost the same for large structures. To show the eectiveness of the proposed method, two numerical examples are considered.