The Best Rank-One Approximation Ratio of a Tensor Space

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 uppe...

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Bibliographic Details
Published in:	SIAM journal on matrix analysis and applications Vol. 32; no. 2; pp. 430 - 442
Main Author:	Qi, Liqun
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.04.2011
Subjects:	Acceleration of convergence Algebra Algorithms Applied mathematics Approximation Eigenvalues Exact sciences and technology Functional analysis Linear and multilinear algebra, matrix theory Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use Lower bound Symmetric tensor Normed space Rank tensors Ordered space Upper bound Numerical analysis Symmetric space Linear algebra Greedy algorithm Convergence rate bounds Best approximation Quotient best rank-one approximation ratio
ISSN:	0895-4798, 1095-7162
Online Access:	Get full text
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