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 |
Keywords:
weakly nonlinear system; \(M\)-matrix; iteration procedure; convergence; fixed-point problemReferences:
| [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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