关于Anderson混合的研究进展  

Research advance on Anderson mixing

作　　者：包承龙 韦福超 BAO Chenglong;WEI Fuchao(Yau Mathematical Sciences Center,Tsinghua University,Beijing 100084,China;Department of Computer Science and Technology,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学丘成桐数学科学中心,北京100084 [2]清华大学计算机科学与技术系,北京100084

出　　处：《中山大学学报（自然科学版）（中英文）》2023年第5期59-66,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家重点研发计划(2021YFA1001300);国家自然科学基金(12271291)。

摘　　要：Anderson混合是一种经典的外推方法,它能利用历史迭代信息加速定点迭代的收敛,在科学计算和机器学习中得到了成功的应用.由于Anderson混合在实践中经常表现出优越的数值性能,在各类应用中围绕Anderson混合的算法设计和理论分析成为近几年的研究热点.本文综述关于Anderson混合的研究进展,重点介绍基于Anderson混合的新算法.Anderson mixing is a classical extrapolation method.It can make use of the information in historical iterations to accelerate the convergence of fixed-point iterations,and has been successfully applied in scientific computing and machine learning.Since Anderson mixing often exhibits superior numerical performance in practice,the algorithm design and theoretical analysis around Anderson mixing in various applications have become hot topics in recent years.This article reviews the research advance on Anderson mixing,and highlights new algorithms based on Anderson mixing.

关 键 词：Anderson混合 定点迭代 KRYLOV子空间方法 拟NEWTON法 

分 类 号：O221.2[理学—运筹学与控制论]