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    An Algorithm for the Convolution of Legendre Series

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    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
    
    Metadata
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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.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/140955835
    ae974a485f413a2113503eed53cd6c53
    10.1137/140955835
    Scopus Count
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