DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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