Study on the preconditioners

✍ Scribed by M. Morimoto

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 377 KB
• Volume: 234
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.12.016

✦ Synopsis

Kotakemori et al. (2002) [2]

have reported that the convergence rate of the iterative method with a preconditioner P m = (I + S max ) was superior to one of the modified Gauss-Seidel methods under a special condition. The authors derived a theorem comparing the Gauss-Seidel method. To remove the requirement for this condition, Morimoto et al. (2004) [4] have proposed the preconditioner P sm = (I + S + S m ). However, it is pointed out that there exists a special matrix that does not satisfy this comparison theorem. To overcome this problem, Kohno et al. (2009) [3] have proposed some preconditioners. In this note, we present a new preconditioner and from numerical results, we show that the convergence rate of the proposed method is better than that of the Gauss-Seidel method with other preconditioners. In addition, we presented the comparison theorem for the proposed preconditioner. We succeeded to overcome two drawbacks mentioned above.