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1994•International Journal of Computer MathematicsRequires access

The upper bound of the spectral radius of M-1N and convergence of some iterative methods

Wang Xinmin, D. J. Evans

Open publisher page 7 citations

Abstract

Using a concise method, different from those in [1-3,7,8] used by K. R. James, M. Martins and Hu Jia-gan, repectively, this paper discusses the upper bounds of the spectral radii of the matarices M-1N and Lyoi which is the AOR type matrix, and gives new results. Based on these conclusions further results for the convergence domains of the AOR and GAOR, SOR and GSOR iterative methods with strictly or irreducibly diagonally dominant matrices are obtained. Finally conditions equivalent to the statement that the matrix is strictly or irreducibly diagonally dominant by rows are established.

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What this paper is about

Using a concise method, different from those in [1-3,7,8] used by K. R. James, M. Martins and Hu Jia-gan, repectively, this paper discusses the upper bounds of the spectral radii of the matarices M-1N and Lyoi which is the AOR type matrix, and gives new results. Based on these conclusions further results for the convergence domains of the AOR and GAOR, SOR and GSOR iterative methods with strictly or irreducibly diagonally dominant matrices are obtained. Finally conditions equivalent to the statement that the matrix is strictly or irreducibly diagonally dominant by rows are established.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Using a concise method, different from those in [1-3,7,8] used by K. R. James, M. Martins and Hu Jia-gan, repectively, this paper discusses the upper bounds of the spectral radii of the matarices M-1N and Lyoi which is the AOR type matrix, and gives new results. Based on these conclusions further results for the convergence domains of the AOR and GAOR, SOR and GSOR iterative methods with strictly or irreducibly diagonally dominant matrices are obtained. Finally conditions equivalent to the statement that the matrix is strictly or irreducibly diagonally dominant by rows are established.

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

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