On the solution of a class of nonlinear systems governed by an \(M\)-matrix (Q444253)
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scientific article; zbMATH DE number 6065424
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solution of a class of nonlinear systems governed by an \(M\)-matrix |
scientific article; zbMATH DE number 6065424 |
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On the solution of a class of nonlinear systems governed by an \(M\)-matrix (English)
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14 August 2012
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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.
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weakly nonlinear system
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\(M\)-matrix
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iteration procedure
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convergence
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fixed-point problem
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