First Advisor

Panayot Vassilevski

Date of Award

6-2019

Document Type

Thesis

Degree Name

Bachelor of Science (B.S.) in Mathematics and University Honors

Department

Mathematics and Statistics

Subjects

Conjugate gradient methods, Parallel processing (Electronic computers), Linear systems, Mathematical optimization

DOI

10.15760/honors.766

Abstract

This paper develops the original conjugate gradient method and the idea of preconditioning a system. I also propose a unique type of additive-Schwarz preconditioner that can be solved in parallel, which creates a speed increase for large systems. To show this, I developed a C++11 linear algebra library used in conjunction with the OpenMP parallel computing library to empirically show a speed increase.

Rights

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Persistent Identifier

https://archives.pdx.edu/ds/psu/29022

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