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The two-stage iteration algorithms based on the shortest distance for low-rank matrix completion

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  • Wen, Rui-Ping
  • Liu, Li-Xia

Abstract

Despite matrix completion requiring the global solution of a non-convex objective, there are many computational efficient algorithms which are effective for a broad class of matrices. Based on these algorithms for matrix completion with given rank problem, we propose a class of two-stage iteration algorithms for general matrix completion in this paper. The inner iteration is the scaled alternating steepest descent algorithm for the fixed-rank matrix completion problem presented by Tanner and Wei (2016), the outer iteration is used two iteration criterions: the gradient norm and the distance between the feasible part with the corresponding part of reconstructed low-rank matrix. The feasibility of the two-stage algorithms are proved. Finally, the numerical experiments show the two-stage algorithms with shorting the distance are more effective than other algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:133-141
    DOI: 10.1016/j.amc.2017.07.024
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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.
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    Cited by:

    1. 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.

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    1. 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.

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