Updating to Optimal Parametric Values by Memory-Dependent Methods: Iterative Schemes of Fractional Type for Solving Nonlinear Equations
Chein-Shan Liu,
Chih-Wen Chang
Abstract:In the paper, two nonlinear variants of the Newton method are developed for solving nonlinear equations. The derivative-free nonlinear fractional type of the one-step iterative scheme of a fourth-order convergence contains three parameters, whose optimal values are obtained by a memory-dependent updating method. Then, as the extensions of a one-step linear fractional type method, we explore the fractional types of two- and three-step iterative schemes, which possess sixth- and twelfth-order convergences when t… Show more
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