Displaying similar documents to “A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems”

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...

Greedy Algorithms for Adaptive Approximation

Albert Cohen (2009)

Bollettino dell'Unione Matematica Italiana

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We discuss the performances of greedy algorithms for two problems of numerical approximation. The first one is the best approximation of an arbitrary function by an N-terms linear combination of simple functions adaptively picked within a large dictionary. The second one is the approximation of an arbitrary function by a piecewise polynomial function on an optimally adapted triangulation of cardinality N. Performance is measured in terms of convergence rate with respect to the number...

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...

Improved approximation of the general soft-capacitated facility location problem

Laurent Alfandari (2007)

RAIRO - Operations Research

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The soft-capacitated facility location problem, where each facility is composed of a variable number of fixed-capacity production units, has been recently studied in several papers, especially in the metric case. In this paper, we only consider the general problem where connection costs do not systematically satisfy the triangle inequality property. We show that an adaptation of the set covering greedy heuristic, where the subproblem is approximately solved by a fully polynomial-time...

From Eckart and Young approximation to Moreau envelopes and vice versa

Jean-Baptiste Hiriart-Urruty, Hai Yen Le (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most . In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.