《Journal of Computational Mathematics》 2010年06期

ON CONTRACTION AND SEMI-CONTRACTION FACTORS OF GSOR METHOD FOR AUGMENTED LINEAR SYSTEMS

【摘要】：正 The generalized successive overrelaxation (GSOR) method was presented and studiedby Bai,Parlett and Wang [Numer.Math.102(2005),pp.1-38] for solving the augmentedsystem of linear equations,and the optimal iteration parameters and the correspondingoptimal convergence factor were exactly obtained.In this paper,we further estimate thecontraction and the semi-contraction factors of the GSOR method.The motivation ofthe study is that the convergence speed of an iteration method is actually decided by thecontraction factor but not by the spectral radius in finite-step iteration computations.Forthe nonsingular augmented linear system,under some restrictions we obtain the contractiondomain of the parameters involved,which guarantees that the contraction factor of theGSOR method is less than one.For the singular but consistent augmented linear system,we also obtain the semi-contraction domain of the parameters in a similar fashion.Finally,we use two numerical examples to verify the theoretical results and the effectiveness of theGSOR method.

 【共引文献】
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 中国硕士学位论文全文数据库 前2条
 1 凌晓锋;解大型稀疏鞍点问题的迭代方法[D];浙江大学;2006年 2 陆群花;大型稀疏线代数方程组的几种数值算法研究[D];兰州大学;2007年
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 >Journal of S... >数学的实践与认识 >Theoretical ... >Journal of C...

 >Department >中南大学数学科学与计算技...

 >Lisa Oberbroeckling >J.-D.Benamou >董华 >Karl Kunisch >刘再明 >Christos Xenophontos
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