Tensor-train numerical integration of multivariate functions with singularities

DOI10.1134/S1995080221070258zbMath1497.65062arXiv2103.12129MaRDI QIDQ2046409

L. I. Vysotsky, Evgenij E. Tyrtyshnikov, Alexander V. Smirnov

Publication date: 18 August 2021

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.12129

zbMATH Keywords

numerical integrationmultivariate integrationmultidimensional integrationtensor trainsampling pointTT-format

Mathematics Subject Classification ID

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

Related Items

FIESTA5: numerical high-performance Feynman integral evaluation

Uses Software

• Cuba
• QUADPACK
• UNCMND
• VEGAS
• pchip
• FIESTA
• pySecDec

Cites Work

• Tensor-Train Decomposition
• TT-cross approximation for multidimensional arrays
• Cuba -- a library for multidimensional numerical integration
• Resolution of singularities for multi-loop integrals
• On selecting a maximum volume sub-matrix of a matrix and related problems
• A new algorithm for adaptive multidimensional integration
• Pseudo-skeleton approximations by matrices of maximal volume
• Incomplete cross approximation in the mosaic-skeleton method
• Approximation of boundary element matrices
• FIESTA4: optimized Feynman integral calculations with GPU support
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Parallel cross interpolation for high-precision calculation of high-dimensional integrals
• An adaptive algorithm for the approximate calculation of multiple integrals
• High-dimensional integration: The quasi-Monte Carlo way
• The double-exponential transformation in numerical analysis
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
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