Efficient methods of optimal eighth and sixteenth order convergence for solving nonlinear equations

被引：0

作者：

Sharma J.R. ^{[1
]}

Kumar S. ^{[1
]}

机构：

[1] Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur

来源：

SeMA Journal | 2018年 / 75卷 / 2期

关键词：

Basins of attraction; Computational efficiency; Multipoint methods; Nonlinear equations; Order of convergence;

D O I：

10.1007/s40324-017-0131-3

中图分类号：

学科分类号：

摘要：

We present simple yet efficient three- and four-point iterative methods for solving nonlinear equations. The methodology is based on fourth order Kung–Traub method and further developed by using rational Hermite interpolation. Three-point method requires four function evaluations and has the order of convergence eight, whereas the four-point method requires the evaluation of five functions and has the order of convergence sixteen, that means, the methods are optimal in the sense of Kung–Traub hypothesis (Kung and Traub, J ACM 21:643–651, 1974). The methods are tested through numerical experimentation. Their performance is compared with already established methods in literature. It is observed that new algorithms are well-behaved and very effective in high precision computations. Moreover, the presented basins of attraction also confirm stable nature of the algorithms. © 2017, Sociedad Española de Matemática Aplicada.

引用

页码：229 / 253

页数：24

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