an:06560382
Zbl 1350.65046
Ahmad, Fayyaz; Tohidi, Emran; Carrasco, Juan A.
A parameterized multi-step Newton method for solving systems of nonlinear equations
EN
Numer. Algorithms 71, No. 3, 631-653 (2016).
00353825
2016
j
65H10 65N22
multi-step iterative methods; multi-step Newton method; systems of nonlinear equations; discretization methods for partial differential equations; nonlinear complex Zakharov system
The authors introduce a new multi-step method solving systems nonlinear equations \(\mathbf{F}(\mathbf{x})=0\), where \(\mathbf{F}: \Gamma \subseteq \mathbb{R}^n \rightarrow \mathbb{R}^r\) is Fr??chet differentiable at \(\mathbf{x}\in\mathrm{interior}(\Gamma)\) with \(\mathbf{F}(\mathbf{x^\ast})=0\) and \(\det(\mathbf{F}'(x^\ast))\neq 0\). They prove that the method needs \(m\) steps to obtain \(m+1\) convergence order. The method is a generalization of the multi-step Newton method based on a parameter \(\theta\). Applying the method for solving the nonlinear complex Zakharov system [\textit{A. H. Bhrawy}, Appl. Math. Comput. 247, 30--46 (2014; Zbl 1339.65188)], the authors show that the appropriate choice of \(\theta\) leads to faster convergence and larger radius of convergence.
Przemys??aw Stpiczy??ski (Lublin)
Zbl 1339.65188