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Convergence of splittings of matrices

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Abstract

In order to investigate the convergence of splittings of matrices, we introduce a concept, where a splitting is (generalized) diagonally dominant. On this basis we prove some necessary and sufficient conditions for the convergence of general splittings of matrices. Much attention is also paid to special iterative methods concerning blockJacobi (BJ), blockGauss-Seidel (BGS), BJOR, BSOR andBAOR iterations, as well as generalizedJacobi (GJ), generalizedGauss-Seidel (GGS), GJOR, GSOR andGAOR iterations. Finally, some sufficient conditions for divergence are given, and we also provide a definition for a splitting to be diagonally weak.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, 210024, Nanjing, People's Republic of China

    Y. Song

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  1. Y. Song
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Song, Y. Convergence of splittings of matrices. Calcolo 30, 91–105 (1993). https://doi.org/10.1007/BF02576175

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  • DOI: https://doi.org/10.1007/BF02576175

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