Abstract
In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order of new method is 2 + 6 ≈ 4.4495 . Numerical experiments are made to show the performance of the new method, which supports the theoretical results.
Highlights
Self-accelerating type method is a kind of efficient iterative method with memory for solving nonlinear equations, which chooses some varying parameters as self-accelerating parameters in the iteration processes
The main purpose of this paper is that a new way is proposed to construct a self-accelerating parameter, which is different from the secant method and interpolation method
A new self-accelerating type method is proposed for solving nonlinear equations, which is a modified scheme of Ren’s method
Summary
Self-accelerating type method is a kind of efficient iterative method with memory for solving nonlinear equations, which chooses some varying parameters as self-accelerating parameters in the iteration processes. By increasing the number of self-accelerating parameters or using interpolation polynomial of high degree to construct self-accelerating parameter, the convergence order and the computational efficiency of self-accelerating type methods can be improved greatly. Zaka et al [9] gave an efficient tri-parametric iterative method by using Newton interpolation polynomial to construct self-accelerating parameter. It is obvious that the secant method and interpolation method are very effective ways to construct self-accelerating parameter All of these researches focused their works on the design of the methods trying to improve their convergence order and computational efficiency. The main purpose of this paper is that a new way is proposed to construct a self-accelerating parameter, which is different from the secant method and interpolation method.
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