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On the solution of a class of nonlinear systems governed by an $$M$$-matrix. (English) Zbl 1248.65052
Summary: We consider a weakly nonlinear system of the form $$(I + \varphi(x)A)x = p$$, where $$\varphi(x)$$ is a real function of the unknown vector $$x$$, and $$(I + \varphi(x)A)$$ is an $$M$$-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure $$(I + \varphi(x_r)A)x_{r+1} = p, r = 0, 1, \dots$$. The global convergence is proved by considering a related fixed-point problem.

##### MSC:
 65H10 Numerical computation of solutions to systems of equations
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##### References:
 [3] DOI: 10.1016/j.amc.2005.12.052 · Zbl 1148.65313 · doi:10.1016/j.amc.2005.12.052 [4] DOI: 10.1080/00207160701650353 · Zbl 1177.65165 · doi:10.1080/00207160701650353 [5] Classics in Applied Mathematics 9 (1994) [6] Applied Numerical Mathematics 37 (3) pp 359– (2001) · Zbl 1022.65061 · doi:10.1016/S0168-9274(00)00052-0
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