Handle URI:
http://hdl.handle.net/10754/597506
Title:
An Algorithm for the Convolution of Legendre Series
Authors:
Hale, Nicholas; Townsend, Alex
Abstract:
An O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N 2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the improved efficiency over the existing algorithm. © 2014 Society for Industrial and Applied Mathematics.
Citation:
Hale N, Townsend A (2014) An Algorithm for the Convolution of Legendre Series. SIAM Journal on Scientific Computing 36: A1207–A1220. Available: http://dx.doi.org/10.1137/140955835.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2014
DOI:
10.1137/140955835
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
Department of Applied Mathematics, University of Stellenbosch, Stellenbosch, 7600, South Africa (nickhale@sun.ac.za, http://nickhale.info). This author's work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK (townsend@maths.ox.ac.uk, http://people.maths.ox.ac.uk/townsend/). This author's work was supported by EPSRC grant EP/P505666/1 and by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant 291068.
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Full metadata record

DC FieldValue Language
dc.contributor.authorHale, Nicholasen
dc.contributor.authorTownsend, Alexen
dc.date.accessioned2016-02-25T12:41:04Zen
dc.date.available2016-02-25T12:41:04Zen
dc.date.issued2014-01en
dc.identifier.citationHale N, Townsend A (2014) An Algorithm for the Convolution of Legendre Series. SIAM Journal on Scientific Computing 36: A1207–A1220. Available: http://dx.doi.org/10.1137/140955835.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/140955835en
dc.identifier.urihttp://hdl.handle.net/10754/597506en
dc.description.abstractAn O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N 2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the improved efficiency over the existing algorithm. © 2014 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipDepartment of Applied Mathematics, University of Stellenbosch, Stellenbosch, 7600, South Africa (nickhale@sun.ac.za, http://nickhale.info). This author's work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK (townsend@maths.ox.ac.uk, http://people.maths.ox.ac.uk/townsend/). This author's work was supported by EPSRC grant EP/P505666/1 and by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant 291068.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectConvolutionen
dc.subjectFourier transformen
dc.subjectLegendre polynomialen
dc.subjectSpherical Bessel functionen
dc.titleAn Algorithm for the Convolution of Legendre Seriesen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversiteit Stellenbosch, Stellenbosch, South Africaen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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