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http://hdl.handle.net/10397/6103
| Title: | The best rank-one approximation ratio of a tensor space | Authors: | Qi, L | Issue Date: | 2011 | Source: | SIAM journal on matrix analysis and applications, 2011, v. 32, no. 2, p. 430–442 | Abstract: | In this paper we define the best rank-one approximation ratio of a tensor space. It turns out that in the finite dimensional case this provides an upper bound for the quotient of the residual of the best rank-one approximation of any tensor in that tensor space and the norm of that tensor. This upper bound is strictly less than one, and it gives a convergence rate for the greedy rank-one update algorithm. For finite dimensional general tensor spaces, third order finite dimensional symmetric tensor spaces, and finite biquadratic tensor spaces, we give positive lower bounds for the best rank-one approximation ratio. For finite symmetric tensor spaces and finite dimensional biquadratic tensor spaces, we give upper bounds for this ratio. | Keywords: | Tensors Best rank-one approximation ratio Bounds |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on matrix analysis and applications | ISSN: | 0895-4798 | EISSN: | 1095-7162 | DOI: | 10.1137/100795802 | Rights: | © 2011 Society for Industrial and Applied Mathematics |
| Appears in Collections: | Journal/Magazine Article |
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