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Tensor-Train Numerical Integration of Multivariate Functions with Singularities
Lobachevskii Journal of Mathematics. 2021. Vol. 42. P. 1608–1621.
Высоцкий Л. И., Смирнов А. В., Тыртышников Е. Е.
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.
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