An Algorithm for the Convolution of Legendre Series | Zendy

Nicholas Hale | Zendy; Alex Townsend | Zendy

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An Algorithm for the Convolution of Legendre Series

Author(s) -

Nicholas Hale,

Alex Townsend

Publication year - 2014

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/140955835

Subject(s) - mathematics , legendre polynomials , convolution (computer science) , legendre function , bessel function , series (stratigraphy) , recurrence relation , convolution theorem , algorithm , chebyshev filter , mathematical analysis , fourier transform , fourier analysis , computer science , paleontology , machine learning , artificial neural network , biology , fractional fourier transform

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

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