Evgeny Tyrtyshnikov, Professor, ShenZhen MSU-BIT University

Hehu Xie, Professor

Tensor-Train Numerical Integration of Multivariate Functions with Singularities

16:00-17:00 July 4(Friday), N733

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.

About the Speaker: Evgeny Tyrtyshnikov is a Russian mathematician, Dr. Sc., Professor, Academician of the Russian Academy of Sciences, and a professor at the Faculty of Computer Science at Moscow State University. He graduated from the faculty of MSU CMC in 1977. Has been working at Moscow State University since 2004. He was awarded the title of Professor in 1996, director of Marchuk Institute of Numerical Mathematics of RAS since 2010, and became the Academician of the Russian Academy of Sciences in 2016. His research fields include linear algebra and its applications, asymptotic analysis of matrix spectra, integral equations of mathematical physics, and computational methods. He has published 6 books and more than 130 scientific articles.