Displaying similar documents to “Low rank Tucker-type tensor approximation to classical potentials”

Exploiting tensor rank-one decomposition in probabilistic inference

Petr Savický, Jiří Vomlel (2007)

Kybernetika

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We propose a new additive decomposition of probability tables – tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one- dimensional tables. Entries in tables are allowed to be any real number, i. e. they can be also negative numbers. The possibility...

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

M. Billaud-Friess, A. Nouy, O. Zahm (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal residual method with a measure of the residual corresponding to the error in a specified solution norm. The residual norm can be designed such that the resulting low-rank approximations are optimal with respect to particular norms of interest, thus allowing...

A Spectral Theory for Tensors

Edinah K. Gnang, Ahmed Elgammal, Vladimir Retakh (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors. Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how...

Latent Semantic Indexing using eigenvalue analysis for efficient information retrieval

Cherukuri Kumar, Suripeddi Srinivas (2006)

International Journal of Applied Mathematics and Computer Science

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Text retrieval using Latent Semantic Indexing (LSI) with truncated Singular Value Decomposition (SVD) has been intensively studied in recent years. However, the expensive complexity involved in computing truncated SVD constitutes a major drawback of the LSI method. In this paper, we demonstrate how matrix rank approximation can influence the effectiveness of information retrieval systems. Besides, we present an implementation of the LSI method based on an eigenvalue analysis for rank...