Comparisons of several algorithms for Toeplitz matrix recovery

Abstract

In this paper, we study algorithms for Toeplitz matrix recovery. Inspired by the singular value thresholding (SVT) algorithm for matrix completion and the alternating directions iterative method, we first propose a new mean value algorithm for Toeplitz matrix recovery. Then we apply our idea to the augmented Lagrange multiplier (ALM) algorithm for matrix recovery and put forward four modified ALM algorithms for Toeplitz matrix recovery. Convergence analysis of the new algorithms is discussed. All the iterative matrices generated by the five algorithms keep a Toeplitz structure that ensures the fast singular value decomposition (SVD) of Toeplitz matrices. Compared with the original algorithms, our algorithms are far superior in the time of SVD, as well as the CPU time.