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You, Zhaoyong; Wang, Chuanlong

A concept of nonlinear block diagonal dominance. (English) Zbl 0886.65052

J. Comput. Appl. Math. 83, No. 1, 1-10 (1997).
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.
Generalized diagonally dominant mappings were introduced and studied by A. Frommer [J. Comput. Appl. Math. 38, No. 1-3, 105-124 (1991; Zbl 0746.65046)].
Reviewer: V.Berinde (Baia Mare)

Cited in 2 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations

Keywords:

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

Citations:

Zbl 0746.65046
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\textit{Z. You} and \textit{C. Wang}, J. Comput. Appl. Math. 83, No. 1, 1--10 (1997; Zbl 0886.65052)
Full Text: DOI

References:

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