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《Journal of Computational Mathematics》 2010年06期
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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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