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Zbl 0886.65052
You, Zhaoyong; Wang, Chuanlong
A concept of nonlinear block diagonal dominance. (English)
[J] J. Comput. Appl. Math. 83, No.1, 1-10 (1997). ISSN 0377-0427

A new concept of diagonal dominance, which generalizes the strictly diagonally dominance for nonlinear functions, called block diagonal dominance, is introduced. Sufficient conditions for a function to be block strictly diagonally dominant as well as applications to block asynchronous iterative methods for approximating fixed points, are also given. \par Generalized diagonally dominant mappings were introduced and studied by {\it A. Frommer} [J. Comput. Appl. Math. 38, No. 1-3, 105-124 (1991; Zbl 0746.65046)].
[V.Berinde (Baia Mare)]

MSC 2000:: *65H10 Systems of nonlinear equations (numerical methods)

Keywords: block strictly diagonally dominant function; Gâteaux-differentiable function; block asynchronous SOR-method

Citations: Zbl 0746.65046

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