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dc.contributor.authorHale, Nicholas
dc.contributor.authorTownsend, Alex
dc.date.accessioned2016-02-25T12:41:04Z
dc.date.available2016-02-25T12:41:04Z
dc.date.issued2014-01
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.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/140955835
dc.identifier.urihttp://hdl.handle.net/10754/597506
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.
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.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectConvolution
dc.subjectFourier transform
dc.subjectLegendre polynomial
dc.subjectSpherical Bessel function
dc.titleAn Algorithm for the Convolution of Legendre Series
dc.typeArticle
dc.identifier.journalSIAM Journal on Scientific Computing
dc.contributor.institutionUniversiteit Stellenbosch, Stellenbosch, South Africa
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04


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