Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme

Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms for manipulating these multi-way arrays are thus required. In this paper, we focus on the best rank-(R1, R2, R3) approximation of third-order t...

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Bibliographic Details
Published in:	SIAM journal on matrix analysis and applications Vol. 32; no. 1; pp. 115 - 135
Main Authors:	Ishteva, Mariya, Absil, P.-A., Van Huffel, Sabine, De Lathauwer, Lieven
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:	Algebra Algebraic geometry Algorithms Approximation Arrays Convergence Cost function Exact sciences and technology Geometry Iterative methods Linear algebra Linear and multilinear algebra, matrix theory Manifolds and cell complexes Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Optimization Sciences and techniques of general use Statistics Studies Tensors Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Cost minimization Second order Product Iteration multilinear algebra Riemann manifold Grassmann manifold Three manifold 65F99 Approximation order Convergence rate Cost function Singular value decomposition Conjugate gradient method 53B20 Approximation Tensor Solving Rank 90C48 15A69 Riemannian manifold Statistics rank reduction Statistical method Array Numerical analysis Scientific computation Function minimization Linear algebra Signal processing Best approximation trust-region scheme 49M37 higher-order tensor
ISSN:	0895-4798, 1095-7162
Online Access:	Get full text
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