Persistent Link:
http://hdl.handle.net/10150/245079
Title:
Solving Fredholm Integral Equations Using Chebyshev Polynomials
Author:
Lerner, Jeremy Neil
Issue Date:
May-2012
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this thesis, we study the approximation of the Fredholm integral equation of the second kind using Chebyshev series expansions. We also modified the resulting algorithms to be suitable for running on a Graphics Processing Unit (GPU). With fixed precision, the results of this method become inaccurate due to the exponential growth of the matrix condition number as number of terms in the series increases. The GPU implementation of the modified algorithm attained a significant speedup compared to the Central Processing Unit (CPU). However, the GPU libraries currently support neither an adaptive step size for integration nor arbitrary precision and therefore experienced larger error than the CPU implementation.
Type:
text; Electronic Thesis
Degree Name:
B.S.
Degree Level:
bachelors
Degree Program:
Honors College; Mathematics
Degree Grantor:
University of Arizona

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleSolving Fredholm Integral Equations Using Chebyshev Polynomialsen_US
dc.creatorLerner, Jeremy Neilen_US
dc.contributor.authorLerner, Jeremy Neilen_US
dc.date.issued2012-05-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this thesis, we study the approximation of the Fredholm integral equation of the second kind using Chebyshev series expansions. We also modified the resulting algorithms to be suitable for running on a Graphics Processing Unit (GPU). With fixed precision, the results of this method become inaccurate due to the exponential growth of the matrix condition number as number of terms in the series increases. The GPU implementation of the modified algorithm attained a significant speedup compared to the Central Processing Unit (CPU). However, the GPU libraries currently support neither an adaptive step size for integration nor arbitrary precision and therefore experienced larger error than the CPU implementation.en_US
dc.typetexten_US
dc.typeElectronic Thesisen_US
thesis.degree.nameB.S.en_US
thesis.degree.levelbachelorsen_US
thesis.degree.disciplineHonors Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
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