Applied and Computational Math Seminar: Numerical tensor-train ranks and tensor displacement structure

Speaker: Tianyi Shi, Cornell University
Title: Numerical tensor-train ranks and tensor displacement structure

Abstract: Tensors often have too many entries to be stored explicitly so it is essential to compress them into data sparse formats. I will identify three methodologies that can be used to explain when a tensor is compressible. Each methodology leads to bounds on the compressibility of certain tensors, partially explaining the abundance of low-rank tensors in applied mathematics. In particular, I will focus on tensors with a so-called displacement structure, showing that solutions to Poisson equations on tensor-product geometries are highly compressible. As the rank bounds are constructive, I will develop an optimal-complexity spectrally-accurate 3D Poisson solver with O(n (log(n))^2 (log(1/epsilon))^2 complexity for a smooth righthand side, where $n\times n\times n$ is the tensor discretization of the solution. 

Time: Wednesday, June 5, 2019, 10:00-11:00am

Place: Exploratory Hall, Room 4106