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A Hybrid Symbolic-Numeric Method for Multiple Integration Based on Tensor-Product Series Approximations

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dc.contributor.authorCarvajal, Orlando Aen
dc.date.accessioned2006-08-22T14:19:53Z
dc.date.available2006-08-22T14:19:53Z
dc.date.issued2004en
dc.date.submitted2004en
dc.description.abstractThis work presents a new hybrid symbolic-numeric method for fast and accurate evaluation of multiple integrals, effective both in high dimensions and with high accuracy. In two dimensions, the thesis presents an adaptive two-phase algorithm for double integration of continuous functions over general regions using Frederick W. Chapman's recently developed Geddes series expansions to approximate the integrand. These results are extended to higher dimensions using a novel Deconstruction/Approximation/Reconstruction Technique (DART), which facilitates the dimensional reduction of families of integrands with special structure over hyperrectangular regions. The thesis describes a Maple implementation of these new methods and presents empirical results and conclusions from extensive testing. Various alternatives for implementation are discussed, and the new methods are compared with existing numerical and symbolic methods for multiple integration. The thesis concludes that for some frequently encountered families of integrands, DART breaks the curse of dimensionality that afflicts numerical integration.en
dc.formatapplication/pdfen
dc.format.extent588541 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10012/1157
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2004, Carvajal, Orlando A. All rights reserved.en
dc.subjectComputer Scienceen
dc.subjectMultiple Integrationen
dc.subjectGeddes Seriesen
dc.subjectSymbolic-Numeric Integrationen
dc.titleA Hybrid Symbolic-Numeric Method for Multiple Integration Based on Tensor-Product Series Approximationsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentSchool of Computer Scienceen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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