Novel alternating update method for low rank approximation of structured matrices

This work is devoted to designing a unified alternating update method for solving a class of structured low rank approximations under the convex and unitarily invariant norm. By the aid of the variational inequality and monotone operator, the proposed method is proved to converge to the solution poi...

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Vydáno v:Applied numerical mathematics Ročník 121; s. 223 - 233
Hlavní autoři: Bai, Jianchao, Li, Jicheng, Dai, Pingfan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2017
Témata:
Alternating update method
Low rank approximation
Structured matrix
System identification
Alternating update method
System identification
Structured matrix
Low rank approximation
ISSN:0168-9274, 1873-5460
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Shrnutí:This work is devoted to designing a unified alternating update method for solving a class of structured low rank approximations under the convex and unitarily invariant norm. By the aid of the variational inequality and monotone operator, the proposed method is proved to converge to the solution point of an equivalent variational inequality with a worst-case O(1/t) convergence rate in a nonergodic sense. We also analyze that the involved subproblems under the Frobenius norm are respectively equivalent to the structured least-squares problem and low rank least-squares problem, where the explicit solutions to some special cases are derived. In order to investigate the efficiency of the proposed method, several examples in system identification are tested to validate that the proposed method can outperform some state-of-the-art methods.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2017.07.001