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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | A1207-A1220 |
| Number of pages | 1 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 36 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 2014 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Department of Applied Mathematics, University of Stellenbosch, Stellenbosch, 7600, South Africa ([email protected], 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 ([email protected], 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.