Tensor-Train Numerical Integration of Multivariate Functions with Singularities

Autor:	Vysotsky, Lev I., Smirnov, Alexander V., Tyrtyshnikov, Eugene E.
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis High Energy Physics - Phenomenology 26B15 15A69
Zdroj:	Lobachevskii J Math 42, 1608-1621 (2021)
Druh dokumentu:	Working Paper
DOI:	10.1134/S1995080221070258
Popis:	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. Comment: 12 pages, 1 PostScript figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.12129 Zobrazit plný text záznamu View this record from Arxiv