Quasioptimality of maximum-volume cross interpolation of tensors
Quasioptimality of maximum-volume cross interpolation of tensors
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension. For nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms. We justify the theoretical results and test the speed and accuracy of the proposed algorithm with convincing numerical experiments.
high-dimensional problems, tensor train format, maximum-volume principle, cross interpolation
217-244
Savostyanov, Dmitry
49d88c5f-b159-4dff-af88-5b9a5ff18322
1 October 2014
Savostyanov, Dmitry
49d88c5f-b159-4dff-af88-5b9a5ff18322
Savostyanov, Dmitry
(2014)
Quasioptimality of maximum-volume cross interpolation of tensors.
Linear Algebra and Its Applications, 458, .
(doi:10.1016/j.laa.2014.06.006).
Abstract
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension. For nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms. We justify the theoretical results and test the speed and accuracy of the proposed algorithm with convincing numerical experiments.
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Submitted date: 8 May 2013
Published date: 1 October 2014
Keywords:
high-dimensional problems, tensor train format, maximum-volume principle, cross interpolation
Organisations:
Magnetic Resonance
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Local EPrints ID: 353749
URI: http://eprints.soton.ac.uk/id/eprint/353749
ISSN: 0024-3795
PURE UUID: 0f3fbdd9-baf5-4000-a7c5-cc50e5649bfa
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Date deposited: 17 Jun 2013 10:20
Last modified: 14 Mar 2024 14:09
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Author:
Dmitry Savostyanov
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