Banach空间中求解方程的homier方法的半局部收敛性

Computational Mathematics and Computer Modeling with Applications (CMCMA) Pub Date : 2022-01-01 DOI:10.52547/cmcma.1.1.63

Samundra Regmi, I. Argyros, S. George, Christopher I. Argyros

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摘要

本文研究了求解Banach空间非线性方程的homier方法的半局部收敛性分析。据我们所知，在Lipschitz条件下没有给出homier的半局部收敛性。我们的目标是在这些条件下推广homier方法在半局部收敛中的适用性。我们只在证明结果的方法中出现的一阶导数上使用了极大化序列和条件。本研究提供了数值实验。

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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On the semi-local convergence of the Homeier method in Banach space for solving equations

In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the ﬁrst derivative which appear on the method for proving our results. Numerical experiments are provided in this study.

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Computational Mathematics and Computer Modeling with Applications (CMCMA)

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