The proxy point method for rank-structured matrices

Dissertation Defense
Friday, October 25, 2019 - 1:30pm for 1.5 hours (actually 80 minutes)
Skiles 311
Xin Xing – School of Mathematics, Georgia Tech – xxing33@gatech.edu
Xin Xing

Rank-structured matrix representations, e.g., H2 and HSS, are commonly used to reduce computation and storage cost for dense matrices defined by interactions between many bodies. The main bottleneck for their applications is the expensive computation required to represent a matrix in a rank-structured matrix format which involves compressing specific matrix blocks into low-rank form.
We focus on the study and application of a class of hybrid analytic-algebraic compression methods, called the proxy point method. We address several critical problems concerning this underutilized method which limit its applicability. A general form of the method is proposed, paving the way for its wider application in the construction of different rank-structured matrices with kernel functions that are more general than those usually used. Further, we extend the applicability of the proxy point method to compress matrices defined by electron repulsion integrals, which accelerates one of the main computational steps in quantum chemistry. 

Committee members: Prof. Edmond Chow (Advisor, School of CSE, Georgia Tech), Prof. David Sherrill (School of Chemistry and Biochemistry, Georgia Tech), Prof. Jianlin Xia (Department of Mathematics, Purdue University), Prof. Yuanzhe Xi (Department of Mathematics, Emory University), and Prof. Haomin Zhou (School of Mathematics, Georgia Tech).