Document Zbl 1497.65062

Vysotsky, L. I.; Smirnov, A. V.; Tyrtyshnikov, E. E.

Tensor-train numerical integration of multivariate functions with singularities. (English) Zbl 1497.65062

Lobachevskii J. Math. 42, No. 7, 1608-1621 (2021).

Summary: 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.

Cited in 1 Document

MSC:

65D32	Numerical quadrature and cubature formulas
41A55	Approximate quadratures
41A63	Multidimensional problems
65D30	Numerical integration

Keywords:

multidimensional integration; multivariate integration; numerical integration; sampling point; tensor train; TT-format

Software:

pySecDec; QUADPACK; FIESTA; VEGAS; UNCMND; pchip; Cuba

Cite Review PDF

Full Text: DOI arXiv

References:

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