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2009•Basic Sciences Journal of Textile UniversitiesRequires access

Convergence theorems for USSOR iterative methods with the precondition (I+C_α)

Weidong Liu

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Abstract

Under the preconditioned matrices P=I+Cα, the new USSOR iterative methods are obtained.By the splitting theory of matrix, when presenting the convergence about the new methods, the comparison theorems will be obtained. This shows that the proper preconditioned matrices can accelerate the rate of convergence. Then a numerical example is given to illustrate the theorems.

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What this paper is about

Under the preconditioned matrices P=I+Cα, the new USSOR iterative methods are obtained.By the splitting theory of matrix, when presenting the convergence about the new methods, the comparison theorems will be obtained. This shows that the proper preconditioned matrices can accelerate the rate of convergence. Then a numerical example is given to illustrate the theorems.

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Available abstract

Under the preconditioned matrices P=I+Cα, the new USSOR iterative methods are obtained.By the splitting theory of matrix, when presenting the convergence about the new methods, the comparison theorems will be obtained. This shows that the proper preconditioned matrices can accelerate the rate of convergence. Then a numerical example is given to illustrate the theorems.

Key concepts: Precondition, Convergence (economics), Mathematics, Applied mathematics, Rate of convergence, Iterative method, Matrix (chemical analysis), Mathematical optimization

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