Toeplitz矩阵压缩恢复的两种中值修正的增广Lagrange乘子算法

Two Modi?ed Augmented Lagrange Multiplier Algorithms with Median Value Toeplitz Matrix Compressive Recovery

增广Lagrange乘子算法是求解矩阵压缩恢复的一种有效迭代方法.为了有效求解Toeplitz矩阵压缩恢复模型,本文提出了两种中值修正的增广Lagrange乘子算法.在新算法中,对增广Lagrange乘子算法每步产生的迭代矩阵进行中值修正并保证其Toeplitz结构.新算法不仅减少了奇异值分解所用的时间和CPU时间,而且获得更精确的迭代矩阵.同时,本中还详细给出了两种新算法的收敛性分析.最后通过数值例子验证了新算法的可行性和有效性,并展示了新算法在计算时间和精度方面比增广Lagrange乘子算法更有优势.

The augmented Lagrange multiplier algorithm is an e?ective iteration method for solving matrix compressive recovery. To solve the Toeplitz matrix compressive recovery model e?ectively, two modi?ed augmented Lagrange multiplier algorithms with median value are proposed in this paper. In the new algorithms, the iterated matrix generated by the augmented Lagrange multiplier algorithm is modi?ed by median value and its Toeplitz structure is guaranteed. The new algorithms not only reduce the SVD time and CPU time, but also obtain a more accurate iterative matrix. Meanwhile, the convergence analysis of the two new algorithms are also given in detail. Finally, the numerical examples are presented to con?rm their feasibility and e?ectiveness. The numerical implementations also show that the new algorithms have advantage over the augmented Lagrange multiplier algorithm in computation time and accuracy.