High-level convergence order accelerators of iterative methods for nonlinear problems

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-07-08 DOI:10.1016/j.apnum.2025.07.003

Alicia Cordero , Renso V. Rojas-Hiciano , Juan R. Torregrosa , Maria P. Vassileva

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引用次数: 0

Abstract

We present an efficient strategy to increase, under certain conditions, the order of convergence of iterative methods to solve nonlinear systems of equations. We analytically compare the new accelerator with others and establish the conditions under which this technique is more efficient. We perform an analysis of the efficiency of some one-step accelerators that increase the convergence order by two units. New concepts about efficiency are introduced which allow us to compare different iterative schemes from other points of view. We demonstrate that our proposal is a good alternative to the existing ones. As a consequence, we propose two new maximally efficient, damped Newton-Traub type schemes of order 5 and 6. These are an improvement of two other maximally efficient methods. Their numerical performance is better than that of known methods of the same order, and we find that it is a very economical way to achieve high order. Some numerical examples confirm the theoretical results.

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非线性问题迭代法的高收敛阶加速器

在一定条件下，我们提出了一种有效的策略来提高求解非线性方程组的迭代方法的收敛阶。通过与其他加速器的分析比较，确定了该技术更有效的条件。我们分析了一些将收敛阶提高两个单位的单步加速器的效率。介绍了有关效率的新概念，使我们能够从其他角度比较不同的迭代方案。我们证明我们的建议是现有建议的一个很好的替代方案。因此，我们提出了两种新的最有效的5阶和6阶阻尼Newton-Traub型格式。这是对另外两种效率最高的方法的改进。它们的数值性能优于已知的同阶方法，是实现高阶的一种非常经济的方法。一些数值算例证实了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.