On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-11-22 DOI:10.1016/j.jco.2023.101817

Ioannis K. Argyros , Santhosh George

引用次数: 0

Abstract

A plethora of applications from diverse disciplines reduce to solving generalized equations involving Banach space valued operators. These equations are solved mostly iteratively, when a sequence is generated approximating a solution provided that certain conditions are valid on the starting point and the operators appearing on the method. Secant-type methods are developed whose specializations reduce to well known methods such as Newton, modified Newton, Secant, Kurchatov and Steffensen to mention a few. Unified local as well as semi-local analysis of these methods is presented using the celebrated contraction mapping principle in combination with the Aubin property of a set valued operator, and generalized continuity assumption on the operators on these methods. Numerical applications complement the theory.

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求解具有Aubin性质的广义方程的牛顿型方法的统一收敛性分析

来自不同学科的大量应用归结为求解涉及巴拿赫空间值算子的广义方程。这些方程大多是迭代求解的，当产生一个序列近似解时，只要在起点和方法上出现的算子上的某些条件是有效的。割线型方法的发展，其专业化减少到众所周知的方法，如牛顿，修正牛顿，割线，Kurchatov和Steffensen举几例。利用著名的收缩映射原理，结合集值算子的Aubin性质，以及这些方法上算子的广义连续性假设，对这些方法进行了统一的局部和半局部分析。数值应用补充了理论。

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.