Tensor-Train Numerical Integration of Multivariate Functions with Singularities

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.

12 pages, 1 PostScript figure

References in corpus (6)

• Cuba - a library for multidimensional numerical integration
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Resolution of singularities for multi-loop integrals
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Parallel cross interpolation for high-precision calculation of high-dimensional integrals

Cited by in corpus (2)

• FIESTA5: numerical high-performance Feynman integral evaluation
• Learning Feynman Diagrams with Tensor Trains