A semi-smoothing augmented Lagrange multiplier algorithm for low-rank Toeplitz matrix completion

Abstract

Abstract The smoothing augmented Lagrange multiplier (SALM) algorithm is a generalization of the augmented Lagrange multiplier algorithm for completing a Toeplitz matrix, which saves computational cost of the singular value decomposition (SVD) and approximates well the solution. However, the communication of numerous data is computationally demanding at each iteration step. In this paper, we propose an accelerated scheme to the SALM algorithm for the Toeplitz matrix completion (TMC), which will reduce the extra load coming from data communication under reasonable smoothing. It has resulted in a semi-smoothing augmented Lagrange multiplier (SSALM) algorithm. Meanwhile, we demonstrate the convergence theory of the new algorithm. Finally, numerical experiments show that the new algorithm is more effective/economic than the original algorithm.

Keywords

• Toeplitz matrix
• Completion
• Augmented Lagrange multiplier
• Data communication