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


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Article Info

DATE

2019-12

AUTHORS

Ruiping Wen, Shuzhen Li, Yonghong Duan

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. More... »

PAGES

83

References to SciGraph publications

  • 1992-11. Shape and motion from image streams under orthography: a factorization method in INTERNATIONAL JOURNAL OF COMPUTER VISION
  • 2009-12. Exact Matrix Completion via Convex Optimization in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 2014-02. Matrix Recipes for Hard Thresholding Methods in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2011-06. Fixed point and Bregman iterative methods for matrix rank minimization in MATHEMATICAL PROGRAMMING
  • 2016-10. A modified augmented lagrange multiplier algorithm for toeplitz matrix completion in ADVANCES IN COMPUTATIONAL MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1186/s13660-019-2033-7

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    http://dx.doi.org/10.1186/s13660-019-2033-7

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