On the complexity of a unified convergence analysis for iterative methods

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-07-11 DOI:10.1016/j.jco.2023.101781

Ioannis K. Argyros , Stepan Shakhno , Samundra Regmi , Halyna Yarmola

引用次数: 1

Abstract

A local and a semi-local convergence of general iterative methods for solving nonlinear operator equations in Banach spaces is developed under ω-continuity conditions. Our approach unifies existing results and provides a new way of studying iterative methods. The main idea is to find a more accurate domain containing the iterates. No extra effort is used to obtain this. Also, the results of the numerical experiments are given that confirm obtained theoretical estimates.

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关于复杂性的一种统一收敛分析迭代方法

给出了在ω-连续条件下求解Banach空间中非线性算子方程的一般迭代方法的局部收敛性和半局部收敛性。我们的方法统一了已有的结果，为研究迭代方法提供了一种新的途径。主要思想是找到包含迭代的更精确的域。不需要额外的努力来获得它。最后给出了数值实验结果，验证了理论估计。

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

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.