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
收藏
页码：327 / 345
页数：19
相关论文
共 50 条
12345