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

Dmitry Savostyanov, Ivan Oseledets

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBN

Abstract

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.

Original languageEnglish
Title of host publication2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011
DOIs
Publication statusPublished - 13 Dec 2011
Event2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011 - Poitiers, France
Duration: 5 Sep 20117 Sep 2011

Publication series

Name2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011

Conference

Conference2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011
CountryFrance
CityPoitiers
Period5/09/117/09/11

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    Savostyanov, D., & Oseledets, I. (2011). Fast adaptive interpolation of multi-dimensional arrays in tensor train format. In 2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011 [6076873] (2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011). https://doi.org/10.1109/nDS.2011.6076873