GENERALIZED NONLINEAR DIAGONAL DOMINANCE AND APPLICATIONS TO ASYNCHRONOUS ITERATIVE METHODS

[摘要] We introduce a concept of generalized diagonal dominance for nonlinear functions. As in the linear case, this brings together several, apparently different classes of nonlinear functions such as strictly diagonally dominant functions and certain M-functions. With our concept we easily obtain a quite far-reaching result on the global convergence of asynchronous iterative methods for finding zeros of nonlinear functions. Special cases include some known and several new convergence results for special iterative methods such as the nonlinear JOR-, SOR- and SSOR-method.

[发布日期] 1991-12-23

[效力级别]  Proceedings Paper

[关键词] DIAGONAL DOMINANCE;SYSTEMS OF NONLINEAR EQUATIONS;M-FUNCTIONS;ASYNCHRONOUS METHODS;PARALLEL NUMERICAL ALGORITHMS