Analyzing the Semilocal Convergence of a Fourth-Order Newton-Type Scheme with Novel Majorant and Average Lipschitz Conditions

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2024-03-13 DOI:10.1134/s1995423924010026

J. P. Jaiswal

引用次数: 0

Abstract

The main focus of this paper is the analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator. The findings contribute to the theoretical understanding of TSNTS in B.S. and have practical implications in various applications, such as integral equation further validating our results.

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分析四阶牛顿式方案的半局部收敛与新的主要和平均 Lipschitz 条件

摘要本文的重点是分析用于寻找巴拿赫空间（B.S.）中非线性算子解的三步牛顿型方案（TSNTS）的半局部收敛性（S.C.）。本文引入了对 TSNTS 的新颖 S.C. 分析，该分析基于算子一阶导数满足广义 Lipschitz 条件 (G.L.C.) 的假设。这些发现有助于从理论上理解 B.S.中的 TSNTS，并在各种应用中具有实际意义，例如积分方程进一步验证了我们的结果。

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

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

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0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.