Toeplitz矩阵填充的尾端修正增广拉格朗日乘子算法  

Tailed-modification augmented Lagrange multiplier algorithm for Toeplitz matrix completion

作　　者：肖云 温瑞萍[1] XIAO Yun;WEN Ruiping(Key Laboratory for Engineering&Computing Science,Shanxi Provincial Department of Education,Taiyuan Normal University,Jinzhong Shanxi 030619)

机构地区：[1]太原师范学院工程科学计算山西省高等学校重点实验室,山西晋中030619

出　　处：《首都师范大学学报（自然科学版）》2022年第5期8-15,共8页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(11371275);山西省自然科学基金项目(201901D211423)。

摘　　要：基于均值的增广拉格朗日乘子(MALM)算法,提出了一种尾端修正的Toeplitz矩阵填充新算法.该算法利用增广拉格朗日乘子(ALM)算法迭代速度较快的优点,对迭代矩阵序列进行结构化与尾端修正.在一定程度上减少了每步均值处理所产生的数据传输量,从而降低了计算代价.同时详细讨论了新算法的收敛性.最后通过数值实验证明了新算法比l步修正的增广垃格朗日乘子(l-MALM)、MALM以及ALM算法在计算时间上有较大程度的减少.Based on the mean augmented Lagrange multiplier(MALM)algorithm,a tail modified Toeplitz matrix completion algorithm is proposed. The algorithm uses the advantage of the augmented Lagrange multiplier(ALM)algorithm to structure and modify the iteration matrix sequence. To some extent,the data transmission generated by each step of mean processing is reduced,and thus reduces the computational cost. The convergence of the new algorithm is discussed in detail. Finally,the numerical experiments show that the new algorithm has a greater reduction in computing time than l-MALM,MALM and ALM algorithm.

关 键 词：TOEPLITZ矩阵 增广拉格朗日乘子算法 均值 矩阵填充 

分 类 号：O241.6[理学—计算数学]