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A Bound for Spectral Radius and Convergence of SOR Iterative Matrices

Zhuan-De Wang

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Abstract

For solving linear equations Ax=b,a new bound for spectral radius of SOR iterative matrices, based on the concept of doubly diagonal dominance is presented.As an application of the bound,a practical convergence condition of SOR method is obtained.The results obtained are an improvement of those in Ref.[1] and suitable for an extended matrix class,i.e.,doubly diagonally dominant matrices.The results arc also generalized to H-matrices.

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What this paper is about

For solving linear equations Ax=b,a new bound for spectral radius of SOR iterative matrices, based on the concept of doubly diagonal dominance is presented.As an application of the bound,a practical convergence condition of SOR method is obtained.The results obtained are an improvement of those in Ref.[1] and suitable for an extended matrix class,i.e.,doubly diagonally dominant matrices.The results arc also generalized to H-matrices.

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Available abstract

For solving linear equations Ax=b,a new bound for spectral radius of SOR iterative matrices, based on the concept of doubly diagonal dominance is presented.As an application of the bound,a practical convergence condition of SOR method is obtained.The results obtained are an improvement of those in Ref.[1] and suitable for an extended matrix class,i.e.,doubly diagonally dominant matrices.The results arc also generalized to H-matrices.

Key concepts: Diagonally dominant matrix, Spectral radius, Mathematics, Convergence (economics), Upper and lower bounds, Diagonal, Matrix (chemical analysis), Iterative method

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