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Toeplitz matrix completion via smoothing augmented Lagrange multiplier algorithm

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

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.

Suggested Citation

  • Wen, Rui-Ping & Li, Shu-Zhen & Zhou, Fang, 2019. "Toeplitz matrix completion via smoothing augmented Lagrange multiplier algorithm," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 299-310.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:299-310
    DOI: 10.1016/j.amc.2019.02.027
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    References listed on IDEAS

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    1. Wen, Rui-Ping & Yan, Xi-Hong, 2015. "A new gradient projection method for matrix completion," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 537-544.
    2. Wen, Rui-Ping & Liu, Li-Xia, 2017. "The two-stage iteration algorithms based on the shortest distance for low-rank matrix completion," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 133-141.
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    Cited by:

    1. Liao, Shenghai & Fu, Shujun & Li, Yuliang & Han, Hongbin, 2023. "Image inpainting using non-convex low rank decomposition and multidirectional search," Applied Mathematics and Computation, Elsevier, vol. 452(C).

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    1. Wen, Rui-Ping & Liu, Li-Xia, 2017. "The two-stage iteration algorithms based on the shortest distance for low-rank matrix completion," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 133-141.

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