基于均值修正的Toeplitz矩阵填充的增广拉格朗日乘子算法  

A MODIFIED AUGMENTED LAGRANGE MULTIPLIER ALGORITHM FOR TOEPLITZ MATRIX COMPLETION BASED ON MEAN VALUE

作　　者：温瑞萍[1] 肖云 王川龙[1] Wen Ruiping;Xiao Yun;Wang Chuanlong(Key Laboratory for Engineering&Computing Science,Shanxi Provincial Department of Education/Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

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

出　　处：《数值计算与计算机应用》2022年第1期61-75,共15页Journal on Numerical Methods and Computer Applications

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

摘　　要：本文基于均值的增广拉格朗日乘子算法,提出了一种快速且具有较高精度的Toeplitz矩阵填充算法.新算法一方面通过均值结构化处理保证迭代后产生的填充矩阵是可行的Toeplitz矩阵,另一方面通过在迭代过程中嵌入修正步而极大地节约了计算时间,得到了更精确的填充矩阵.同时讨论了新算法的收敛性,最后通过数值实验表明新算法比基于均值的增广Lagrange乘子算法(MALM)和增广Lagrange乘子算法(ALM)在时间和精度上均有改进.In this paper,based on the augmented Lagrange multiplier algorithm with mean value,a faster and higher-precision algorithm for completing Toeplitz matrix is proposed.The new algorithm not only ensures that the filling matrix generated by iteration is feasible after means processing,but also saves the computing time by modifying thchnique in the iteration process and obtains more effective approximation to solution in precision.Meanwhile,the convergence of the new algorithm is established.Finally,the numerical experiment show that the new algorithm covers shorter computing time and has better precision than the augmented Lagrange multiplier algorithm and its improved algorithm based on mean value for Toeplitz matrix completion.

关 键 词：Toeplitz矩阵填充 增广拉格朗日乘子算法 均值 

分 类 号：O151.21[理学—数学]