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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 |
Issue Date: | 2012 | Source: | SIAM journal on matrix analysis and applications, 2012, v. 33, no. 3, p. 806–821 | 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. | Keywords: | Symmetric tensor The best rank-1 approximation The best symmetric rank-1 approximation Power algorithm |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on matrix analysis and applications | 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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Zhang_Best_Rank-1_Approximation.pdf | 258.49 kB | Adobe PDF | View/Open |
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