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A Convergence Theorem of AOR Iteration Method

MA Ming-ze

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Abstract

AOR iteration method for solving linear system are studied,when coefficient matrix is α-chain diagonal strictly dominance and doubly diagonal strictly dominance,and a convergence theorem and some corollaries are given.Results obtained is applicable for diagonal strictly dominance matrix,and for generalized diagonal strictly dominance matrix also.The results not only is that problem of estimates of upper bounds of the spectral radius for some iteration matrices is solved but also convenient for apply.Finally,a numerical example is given for illustrating advantage of results.

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What this paper is about

AOR iteration method for solving linear system are studied,when coefficient matrix is α-chain diagonal strictly dominance and doubly diagonal strictly dominance,and a convergence theorem and some corollaries are given.Results obtained is applicable for diagonal strictly dominance matrix,and for generalized diagonal strictly dominance matrix also.The results not only is that problem of estimates of upper bounds of the spectral radius for some iteration matrices is solved but also convenient for apply.Finally,a numerical example is given for illustrating advantage of results.

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Available abstract

AOR iteration method for solving linear system are studied,when coefficient matrix is α-chain diagonal strictly dominance and doubly diagonal strictly dominance,and a convergence theorem and some corollaries are given.Results obtained is applicable for diagonal strictly dominance matrix,and for generalized diagonal strictly dominance matrix also.The results not only is that problem of estimates of upper bounds of the spectral radius for some iteration matrices is solved but also convenient for apply.Finally,a numerical example is given for illustrating advantage of results.

Key concepts: Mathematics, Diagonal, Diagonally dominant matrix, Spectral radius, Applied mathematics, Diagonal matrix, Convergence (economics), Dominance (genetics)

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