Solving Fredholm Integral Equations Using Chebyshev Polynomials
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 inaccur...
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The University of Arizona.
2012
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| Online Access: | http://hdl.handle.net/10150/245079 |
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ndltd-arizona.edu-oai-arizona.openrepository.com-10150-2450792015-10-23T04:57:33Z Solving Fredholm Integral Equations Using Chebyshev Polynomials Lerner, Jeremy Neil 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. 2012-05 text Electronic Thesis http://hdl.handle.net/10150/245079 en 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. The University of Arizona. |
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NDLTD |
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en |
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NDLTD |
| description |
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. |
| author |
Lerner, Jeremy Neil |
| spellingShingle |
Lerner, Jeremy Neil Solving Fredholm Integral Equations Using Chebyshev Polynomials |
| author_facet |
Lerner, Jeremy Neil |
| author_sort |
Lerner, Jeremy Neil |
| title |
Solving Fredholm Integral Equations Using Chebyshev Polynomials |
| title_short |
Solving Fredholm Integral Equations Using Chebyshev Polynomials |
| title_full |
Solving Fredholm Integral Equations Using Chebyshev Polynomials |
| title_fullStr |
Solving Fredholm Integral Equations Using Chebyshev Polynomials |
| title_full_unstemmed |
Solving Fredholm Integral Equations Using Chebyshev Polynomials |
| title_sort |
solving fredholm integral equations using chebyshev polynomials |
| publisher |
The University of Arizona. |
| publishDate |
2012 |
| url |
http://hdl.handle.net/10150/245079 |
| work_keys_str_mv |
AT lernerjeremyneil solvingfredholmintegralequationsusingchebyshevpolynomials |
| _version_ |
1718101631509200896 |