Toeplitz matrix completion via a low-rank approximation algorithm

Abstract

Abstract In this paper, we propose a low-rank matrix approximation algorithm for solving the Toeplitz matrix completion (TMC) problem. The approximation matrix was obtained by the mean projection operator on the set of feasible Toeplitz matrices for every iteration step. Thus, the sequence of the feasible Toeplitz matrices generated by iteration is of Toeplitz structure throughout the process, which reduces the computational time of the singular value decomposition (SVD) and approximates well the solution. On the theoretical side, we provide a convergence analysis to show that the matrix sequences of iterates converge. On the practical side, we report the numerical results to show that the new algorithm is more effective than the other algorithms for the TMC problem.

Keywords

• Matrix completion
• Toeplitz matrix
• Low-rank
• Mean projection operator