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| 基于均值的Toeplitz矩阵填充的子空间算法 | |
| 引用本文： | 刘丽霞,王川龙. 基于均值的Toeplitz矩阵填充的子空间算法[J]. 计算数学, 2017, 39(2): 179-188 |
| 作者姓名： | 刘丽霞 王川龙 |
| 作者单位： | 1. 太原理工大学数学学院, 太原 030024; 2. 太原师范学院工程科学计算山西省高等学校重点实验室, 太原 030012 |
| 基金项目： | 国家自然科学基金（11371275）. |
| 摘 要： | 本文提出一种基于均值的Toeplitz矩阵填充的子空间算法.通过在左奇异向量空间中对已知元素的最小二乘逼近,形成了新的可行矩阵;并利用对角线上的均值化使得迭代后的矩阵保持Toeplitz结构,从而减少了奇异向量空间的分解时间.理论上,证明了在一定条件下该算法收敛于一个低秩的Toeplitz矩阵.通过不同已知率的矩阵填充数值实验展示了Toeplitz矩阵填充的新算法比阈值增广Lagrange乘子算法在时间上和精度上更有效. |
| 关 键 词： | 矩阵填充 Toeplitz矩阵 子空间 可行序列 均值 |
THE SUBSPACE ALGORITHM WITH MEAN VALUE FOR TOEPLITZ MATRIX COMPLETION |
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| Liu Lixia,Wang Chuanlong. THE SUBSPACE ALGORITHM WITH MEAN VALUE FOR TOEPLITZ MATRIX COMPLETION[J]. Mathematica Numerica Sinica, 2017, 39(2): 179-188 | |
| Authors: | Liu Lixia Wang Chuanlong |
| Affiliation: | 1. Institution of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China; 2. Higher Education Key Laboratory of Engineering Science Computing in Shanxi Province, Taiyuan Normal University, Taiyuan 030012, China |
| Abstract: | This paper proposes a subspace algorithm with mean value for the Toeplitz matrix completion.By the least squares approximation to the known entries in the left singular vector space,this algorithm forms a new feasible matrix,and the matrices generated by iteration keep Toeplitz structure by making use of averaging the diagonal entries.So that,the new algorithm reduces the time of decomposition in the singular vector space.In theory,we prove that the algorithm converges to a Toeplitz matrix with low rank under reasonable conditions.Finally,numerical experiments with different known entry ratio show the new algorithm can be faster and achieve higher precision than the ALM (augmented Lagrange multiplier) algorithm for Toeplitz matrix completion. |
| Keywords: | matrix completion Toeplitz Matrix subspace feasible sequence mean value |
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