求解Einstein-积张量方程的混合贪婪随机坐标下降法  

HYBRID GREEDY RANDOMIZED COORDINATE DESCENT METHOD FOR SOLVING TENSOR EQUATION ACCOMPANIED BY EINSTEIN PRODUCT

作　　者：谢亚君 马昌凤 Xie Yajun;Ma Changfeng(Institute of Science and Technology,Fuzhou University of International Studies and Trade,Changle 350202,China;College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350007,China)

机构地区：[1]福州外语外贸学院理工学院,长乐350202 [2]福建师范大学数学与信息学院,福州350007

出　　处：《数值计算与计算机应用》2021年第4期323-336,共14页Journal on Numerical Methods and Computer Applications

基　　金：福建省自然科学基金项目(2019J01879);福建省高校新世纪优秀人才计划项目(闽教科[2017]52)资助.

摘　　要：贪婪随机坐标下降法是当前提出的求解最小二乘问题的有效方法.本文通过引入“残量最大下降指标”,给出了贪婪随机坐标下降法的修正版本及一个有效的两步混合加速算法.同时.将这些改进的有效算法用来求解带有Einstein-积的张量方程.理论及数值实验都充分验证了所提出算法的可行性和有效性.Greedy randomized coordinate descent method is an efficient method in present for solving large least-square problem.By introducing the‘index of maximum decline of residual error,,in this paper,a modified version of greedy randomized coordinate descent method and a two-step hybrid approach are first investigated.Meanwhile,the modified methods are utilized to solve the tensor equation with Einstein-product.Theory and some numerical experiments illustrate the feasibility and efficiency of the proposed method.

关 键 词：贪婪随机坐标下降法 最快残量下降指标 混合加速算法 Einstein-积 张量方程 

分 类 号：O183.2[理学—数学]