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2009•jOURNAL OF southwest University for NationalitiesRequires access

Generalized symmetic accelerated overrelaxation method and convergence theorem for the large and sparse augmented system

Da‐Wei Chang

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Abstract

In this paper,generalized SAOR method with uncertain parameters is considerded for the large and sparse saddle point problems(GSAOR).This new method is based on the spliting form of the coefficient matrix,and then the function equation among the eigenvalues of the iteration matrix of the GSAOR method and the precontion matrix and also parameters is established.Furthermore,the necessary and sufficient condition for the convergence of the GSAOR method is derived by giving the restrictions imposed on the parameters(In this paper,we only focus on the situation in which the parameter γ is equal to 2).Finally,a numerical example is given to illustrate the accuracy of the theorem results.

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What this paper is about

In this paper,generalized SAOR method with uncertain parameters is considerded for the large and sparse saddle point problems(GSAOR).This new method is based on the spliting form of the coefficient matrix,and then the function equation among the eigenvalues of the iteration matrix of the GSAOR method and the precontion matrix and also parameters is established.Furthermore,the necessary and sufficient condition for the convergence of the GSAOR method is derived by giving the restrictions imposed on the parameters(In this paper,we only focus on the situation in which the parameter γ is equal to 2).Finally,a numerical example is given to illustrate the accuracy of the theorem results.

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Available abstract

In this paper,generalized SAOR method with uncertain parameters is considerded for the large and sparse saddle point problems(GSAOR).This new method is based on the spliting form of the coefficient matrix,and then the function equation among the eigenvalues of the iteration matrix of the GSAOR method and the precontion matrix and also parameters is established.Furthermore,the necessary and sufficient condition for the convergence of the GSAOR method is derived by giving the restrictions imposed on the parameters(In this paper,we only focus on the situation in which the parameter γ is equal to 2).Finally,a numerical example is given to illustrate the accuracy of the theorem results.

Key concepts: Eigenvalues and eigenvectors, Mathematics, Saddle point, Applied mathematics, Convergence (economics), Focus (optics), Matrix (chemical analysis), Saddle

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