KAUST Grant NumberKUK-C1-013-04
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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.
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.
SponsorsDepartment of Applied Mathematics, University of Stellenbosch, Stellenbosch, 7600, South Africa (email@example.com, 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 (firstname.lastname@example.org, 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.