Abstract: The augmented Lagrange multiplier algorithm is an effective iteration method for solving matrix compressive recovery. To solve the Toeplitz matrix compressive recovery model effectively, two modified 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 modified 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 confirm their feasibility and effectiveness. The numerical implementations also show that the new algorithms have advantage over the augmented Lagrange multiplier algorithm in computation time and accuracy.

Key words: compressive recovery, Toeplitz matrix, augmented Lagrange multiplier algorithm