Convergence analysis of the Halpern iteration with adaptive anchoring parameters

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2023-05-17 DOI:10.1090/mcom/3851

Songnian He, Hong-Kun Xu, Qiao-Li Dong, Na Mei

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引用次数: 0

Abstract

We propose an adaptive way to choose the anchoring parameters for the Halpern iteration to find a fixed point of a nonexpansive mapping in a real Hilbert space. We prove strong convergence of this adaptive Halpern iteration and obtain the rate of asymptotic regularity at least O ( 1 / k ) O(1/k) , where k k is the number of iterations. Numerical experiments are also provided to show advantages and outperformance of our adaptive Halpern algorithm over the standard Halpern algorithm.

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自适应锚定参数下Halpern迭代的收敛性分析

提出了一种自适应选择锚定参数的方法，用于在实数Hilbert空间中寻找非扩张映射的不动点。证明了该自适应Halpern迭代的强收敛性，得到了渐近正则性速率至少为O(1/k) O(1/k)，其中k k为迭代次数。数值实验显示了自适应Halpern算法相对于标准Halpern算法的优点和优越性。

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

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.