Tensor-Train Numerical Integration of Multivariate Functions with Singularities
Numerical Analysis
2021-08-23 v1 Numerical Analysis
High Energy Physics - Phenomenology
Abstract
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to overcome this problem. Tensor-train decomposition of a tensor approximating the integrand is constructed and used to evaluate a multivariate quadrature formula. We show how to deal with singularities in the integration domain and conduct theoretical analysis of the integration accuracy. The reference open-source implementation is provided.
Cite
@article{arxiv.2103.12129,
title = {Tensor-Train Numerical Integration of Multivariate Functions with Singularities},
author = {Lev I. Vysotsky and Alexander V. Smirnov and Eugene E. Tyrtyshnikov},
journal= {arXiv preprint arXiv:2103.12129},
year = {2021}
}
Comments
12 pages, 1 PostScript figure