Displaying similar documents to “Low-rank tensor representation of Slater-type and Hydrogen-like orbitals”

Low rank Tucker-type tensor approximation to classical potentials

B. Khoromskij, V. Khoromskaia (2007)

Open Mathematics

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This paper investigates best rank-(r 1,..., r d) Tucker tensor approximation of higher-order tensors arising from the discretization of linear operators and functions in ℝd. Super-convergence of the best rank-(r 1,..., r d) Tucker-type decomposition with respect to the relative Frobenius norm is proven. Dimensionality reduction by the two-level Tucker-to-canonical approximation is discussed. Tensor-product representation of basic multi-linear algebra operations is considered, including...

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...

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...