Comparisons of several algorithms for Toeplitz matrix recovery

In this paper, we study algorithms for Toeplitz matrix recovery. Inspired by the singular value thresholding (SVT) algorithm for matrix completion and the alternating directions iterative method, we first propose a new mean value algorithm for Toeplitz matrix recovery. Then we apply our idea to the...

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Veröffentlicht in:Computers & mathematics with applications (1987) Jg. 71; H. 1; S. 133 - 146
Hauptverfasser: Wang, Chuan-Long, Li, Chao, Wang, Jin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.01.2016
Schlagworte:
Algorithms
Augmented Lagrange multiplier
Central processing units
Convergence
Iterative methods
Lagrange multipliers
Mathematical models
Matrix recovery
Mean value
Recovery
Singular value decomposition
Toeplitz matrix
Augmented Lagrange multiplier
Mean value
Toeplitz matrix
Matrix recovery
ISSN:0898-1221, 1873-7668
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Zusammenfassung:In this paper, we study algorithms for Toeplitz matrix recovery. Inspired by the singular value thresholding (SVT) algorithm for matrix completion and the alternating directions iterative method, we first propose a new mean value algorithm for Toeplitz matrix recovery. Then we apply our idea to the augmented Lagrange multiplier (ALM) algorithm for matrix recovery and put forward four modified ALM algorithms for Toeplitz matrix recovery. Convergence analysis of the new algorithms is discussed. All the iterative matrices generated by the five algorithms keep a Toeplitz structure that ensures the fast singular value decomposition (SVD) of Toeplitz matrices. Compared with the original algorithms, our algorithms are far superior in the time of SVD, as well as the CPU time.
Bibliographie:ObjectType-Article-1
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2015.11.010