Doctoral Dissertations
Date of Award
8-2023
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Computer Science
Major Professor
Jack J. Dongarra
Committee Members
Piotr R. Luszczek, Michael W. Berry, Michael A. Heroux
Abstract
There is a growing performance gap between computation and communication on modern computers, making it crucial to develop algorithms with lower latency and bandwidth requirements. Because systems of linear equations are important for numerous scientific and engineering applications, I have studied several approaches for reducing communication in those problems. First, I developed optimizations to dense LU with partial pivoting, which downstream applications can adopt with little to no effort. Second, I consider two techniques to completely replace pivoting in dense LU, which can provide significantly higher speedups, albeit without the same numerical guarantees as partial pivoting. One technique uses randomized preprocessing, while the other is a novel combination of block factorization and additive perturbation. Finally, I investigate using mixed precision in GMRES for solving sparse systems, which reduces the volume of data movement, and thus, the pressure on the memory bandwidth.
Recommended Citation
Lindquist, Neil S., "Reducing Communication in the Solution of Linear Systems. " PhD diss., University of Tennessee, 2023.
https://trace.tennessee.edu/utk_graddiss/8569
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons