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
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491