求解多约束矩阵最小二乘问题的数值方法  

A MM-Dykstra Method for Solving Least Squares Problem of Multi-Constrained Matrix Equation

作　　者：吕照美 刘新国[1] Lv Zhaomei;Liu Xinguo(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第10期161-166,共6页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11871444)资助。

摘　　要：本文研究了三约束矩阵最小二乘问题。首先给出了该问题的双约束等价形式,并讨论了问题的可解性和最优性条件。其次,将Dykstra算法和MM方法相结合,得到了一种新的迭代解法。最后,通过数值实验验证了新方法的有效性。In this paper,we deal with the triple-constrained least squares problem of matrix equation AXB=C.An equivalent but simplified form of the problem is obtained,and the conditions on solvability and optimality are presented.Combining Dykstra’s algorithm with Majorize-Minimize algorithm we propose a new solution.Preliminary numerical results are given to illustrate the performances of the proposed iterative method.

关 键 词：Dyksrta算法 Majorize-Minimize算法 可解性 最优性条件 初始点 

分 类 号：O241.6[理学—计算数学]