Abstract
The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton–Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences. Consequently, weaker sufficient convergence criteria and more accurate error estimates are retrieved. A special case of weak conditions is also considered.
Highlights
In particular systems of nonlinear algebraic or transcendental equations, arise often when numerical methods are used for solving applied problems
It requires differentiability of the nonlinear function. This is not a requirement for difference methods [1,2,3,4]. They can be applied to equations with a nondifferentiable function [5]
The nonlinear function can be represented as the sum of the differentiable and nondifferentiable parts
Summary
In particular systems of nonlinear algebraic or transcendental equations, arise often when numerical methods are used for solving applied problems. They can be applied to equations with a nondifferentiable function [5]. We use Newton–Kurchatov method [8,13,14,15,16] for solving Equation (1) numerically x n +1 = x n − A −
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