A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds  

作　　者：Teng-Teng Yao Xiao-Qing Jin Zhi Zhao 

机构地区：[1]Department of Mathematics,School of Sciences,Zhejiang University of Science and Technology,Hangzhou 310023,China [2]Department of Mathematics,University of Macao,Macao 999078,SAR,China [3]Department of Mathematics,School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第4期954-967,共14页高等学校计算数学学报（英文版）

基　　金：the first author is supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY21A010004);the National Natural Science Foundation of China(Grant No.11701514);The research of the second author is supported by the research grants MYRG2019-00042-FST and CPG2023-00023-FST from University of Macao;The research of the third author is supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY21A010010);the National Natural Science Foundation of China(Grant No.11601112).

摘　　要：The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this paper.To solve this kind of problem,we propose a modified Riemannian Mann algorithm with inertial effect.Under the assumption of existence of fixed points of the nonexpansive mapping,the global convergence of the proposed algorithm is established.To show the efficiency of the proposed algorithm,numerical comparisons with some existing algorithms are reported.

关 键 词：Nonexpansive mapping Hadamard manifold fixed point inertial Mann algorithm 

分 类 号：O18[理学—数学]