Theses and Dissertations - UTRGV

Date of Award

5-2022

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Andras Balogh

Second Advisor

Dr. Dambaru Bhatta

Third Advisor

Dr. Tamer Oraby

Abstract

Hadamard matrices are square matrices with +1 and -1 entries and with columns that are mutually orthogonal. The applications include signal processing and quantum computing. There are several methods for constructing Hadamard matrices of order 2k for every positive integer k. The Hadamard conjecture proposes that there are also Hadamard matrices of order 4k for every positive integer k. We use a genetic algorithm to construct (search for) Hadamard Matrices. The initial population of random matrices is generated to have a balanced number of +1 and -1 entries in each column. Several fitness functions are implemented exploiting the basic matrix property that QTQ is diagonal if and only if the columns of matrix Q are orthogonal. The crossover process creates offspring matrix population by exchanging columns of the parent matrix population. The mutation process flips +1 and -1 entry pairs in random columns, several methods were implemented to achieve this. The use of CuPy library in Python on graphics processing units enables us to handle populations of thousands of matrices and matrix operations in parallel.

Comments

Copyright 2022 Raven I. Ruiz. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/gpu-accelerated-genetic-algorithm-construction/docview/2699732021/se-2?accountid=7119

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