CONVERGENCE ANALYSIS OF THE HALPERN ITERATION WITH ADAPTIVE ANCHORING PARAMETERS

被引：2

作者：

He, Songnian ^{[1
]}

Xu, Hong-kun ^{[2
,3
]}

Dong, Qiao-li ^{[4
]}

Mei, Na ^{[4
]}

机构：

[1] Civil Aviat Univ China, Coll Sci, Tianjin Key Lab Adv Signal Proc, Tianjin 300300, Peoples R China

[2] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Peoples R China

[3] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China

[4] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

来源：

MATHEMATICS OF COMPUTATION | 2023年

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Halpern iteration; fixed point; adaptive anchoring parameter; rate of asymptotic regularity; FIXED-POINTS; ALGORITHMS; SHRINKAGE;

D O I：

10.1090/mcom/3851

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. 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), where 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.

引用

页码：327 / 345

页数：19

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