Document Type

Thesis

Degree Name

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

Department

Mathematics

First Advisor

Panayot Vassilevski

Subjects

Conjugate gradient methods, Numerical analysis, Mathematical optimization, Iterative methods (Mathematics)

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.

Persistent Identifier

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

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