Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5954
Title: The best rank-1 approximation of a symmetric tensor and related spherical optimization problems
Authors: Zhang, X
Ling, C
Qi, L 
Keywords: Symmetric tensor
The best rank-1 approximation
The best symmetric rank-1 approximation
Power algorithm
Issue Date: 2012
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on matrix analysis and applications, 2012, v. 33, no. 3, p. 806–821 How to cite?
Journal: SIAM journal on matrix analysis and applications 
Abstract: In this paper, we show that for a symmetric tensor, its best symmetric rank-1 approximation is its best rank-1 approximation. Based on this result, a positive lower bound for the best rank-1 approximation ratio of a symmetric tensor is given. Furthermore, a higher order polynomial spherical optimization problem can be reformulated as a multilinear spherical optimization problem. Then, we present a modified power algorithm for solving the homogeneous polynomial spherical optimization problem. Numerical results are presented, illustrating the effectiveness of the proposed algorithm.
URI: http://hdl.handle.net/10397/5954
ISSN: 0895-4798
EISSN: 1095-7162
DOI: 10.1137/110835335
Rights: © 2012 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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