Variable projection for affinely structured low-rank approximation in weighted 2-norms

被引：31

作者：

Usevich, Konstantin ^{[1
]}

Markovsky, Ivan ^{[1
]}

机构：

[1] Vrije Univ Brussel, Dept ELEC, B-1050 Brussels, Belgium

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 272卷

基金：

欧洲研究理事会;

关键词：

Structured low-rank approximation; Variable projection; Mosaic Hankel matrices; Weighted; 2-norm; Fixed elements; Computational complexity; TOTAL LEAST-SQUARES; BLOCK TOEPLITZ MATRICES; ALGORITHM; SOFTWARE; INVERSES;

D O I：

10.1016/j.cam.2013.04.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The structured low-rank approximation problem for general affine structures, weighted 2-norms and fixed elements is considered. The variable projection principle is used to reduce the dimensionality of the optimization problem. Algorithms for evaluation of the cost function, the gradient and an approximation of the Hessian are developed. For m x n mosaic Hankel matrices the algorithms have complexity O(m(2)n). (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：430 / 448

页数：19

共 25 条

[1]

Absil PA, 2008, OPTIMIZATION ALGORITHMS ON MATRIX MANIFOLDS, P1

[2]

[Anonymous], SIAM J MATRIX ANAL A

[3]

BORSDORF R., 2012, THESIS U MANCHESTER

[4]

Boyd S., 2004, CONVEX OPTIMIZATION, VFirst, DOI DOI 10.1017/CBO9780511804441

[5] STRUCTURED TOTAL LEAST-SQUARES AND L2 APPROXIMATION-PROBLEMS [J].

DEMOOR, B .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 188 :163-205

[6]

Golub G. H., 1996, MATRIX COMPUTATIONS

[7] DIFFERENTIATION OF PSEUDO-INVERSES AND NONLINEAR LEAST-SQUARES PROBLEMS WHOSE VARIABLES SEPARATE [J].

GOLUB, GH ;

PEREYRA, V .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (02) :413-432

[8] A Gauss-Newton-like optimization algorithm for ''weighted'' nonlinear least-squares problems [J].

Guillaume, P ;

Pintelon, R .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1996, 44 (09) :2222-2228

[9] GENERALIZED INVERSES OF HANKEL AND TOEPLITZ MOSAIC MATRICES [J].

HEINIG, G .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 216 :43-59

[10]

Heinig G, 1984, Algebraic methods for Toeplitz-like matrices and operators, V1st

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