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Solution of Large Sparse Nonlinear Systems by Monotone Convergent Iterations and Applications
Author(s) -
ElSeoud S. Abou,
Törnig W.
Publication year - 1983
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19830630205
Subject(s) - diagonally dominant matrix , monotonic function , mathematics , monotone polygon , nonlinear system , diagonal , convergence (economics) , gauss–seidel method , boundary value problem , iterative method , mathematical analysis , mathematical optimization , pure mathematics , geometry , invertible matrix , physics , quantum mechanics , economics , economic growth
Abstract In this paper we describe a family of Gauss‐Seidel‐iterations for the solution of large sparse nonlinear systems of equations Fx = 0. The mapping F is off‐diagonally antitone and strictly diagonally isotone. For suitable starting vectors every method of this family is monotonically convergent with respect to both sides. The iteration processes will be applied among others to the numerical solution of boundary value problems of quasilinear potential equations.