An Algorithm for the Convolution of Legendre Series

Nicholas Hale, Alex Townsend

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)A1207-A1220
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number3
StatePublished - Jan 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Department of Applied Mathematics, University of Stellenbosch, Stellenbosch, 7600, South Africa (, 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 (, 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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