Toeplitz matrix completion via smoothing augmented Lagrange multiplier algorithm

Rui-Ping Wen, Shu-Zhen Li and Fang Zhou

Applied Mathematics and Computation, 2019, vol. 355, issue C, 299-310

Abstract: Toplitz matrix completion (TMC) is to fill a low-rank Toeplitz matrix from a small subset of its entries. Based on the augmented Lagrange multiplier (ALM) algorithm for matrix completion, in this paper, we propose a new algorithm for the TMC problem using the smoothing technique of the approximation matrices. The completion matrices generated by the new algorithm are of Toeplitz structure throughout iteration, which save computational cost of the singular value decomposition (SVD) and approximate well the solution. Convergence results of the new algorithm are proved. Finally, the numerical experiments show that the augmented Lagrange multiplier algorithm with smoothing is more effective than the original ALM and the accelerated proximal gradient (APG) algorithms.

Keywords: Toeplitz matrix; Augmented Lagrange multiplier; Matrix completion; Smoothing (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:355:y:2019:i:c:p:299-310

DOI: 10.1016/j.amc.2019.02.027

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