An Algorithm for the Convolution of Legendre Series

Hale, Nicholas; Townsend, Alex

Type

Article

Authors

Hale, Nicholas
Townsend, Alex

KAUST Grant Number

KUK-C1-013-04

Date

2014-01

Permanent link to this record

http://hdl.handle.net/10754/597506

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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.

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.