Fast adaptive interpolation of multi-dimensional arrays in tensor train format

Using recently proposed tensor train format for the representation of multi-dimensional dense arrays (tensors) we develop a fast interpolation method to approximate the given tensor by using only a small number of its elements. The algorithm is based on DMRG scheme, known among the quantum chemistry...

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Bibliographic Details
Published inThe 2011 International Workshop on Multidimensional (nD) Systems pp. 1 - 8
Main Authors Savostyanov, D., Oseledets, I.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2011
Subjects
Approximation algorithms
Indexes
Interpolation
Least squares approximation
Matrix decomposition
Tensile stress
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Summary:Using recently proposed tensor train format for the representation of multi-dimensional dense arrays (tensors) we develop a fast interpolation method to approximate the given tensor by using only a small number of its elements. The algorithm is based on DMRG scheme, known among the quantum chemistry society. It is modified to make an interpolation on the adaptive set of tensor elements. The latter is selected using the maximum-volume principle which was previously used for the cross approximation schemes for matrices and 3-tensors. The numerical examples includes the interpolation of one- and many-dimensional functions on the uniform grids.
ISBN:9781612848150
161284815X
DOI:10.1109/nDS.2011.6076873