Representation of sparse Legendre expansions

Authors:
Thomas Peter;Gerlind Plonka;Daniela RoşCa
Affiliations:
University of Göttingen, Institute for Numerical and Applied Mathematics, Lotzestr. 16-18, 37083 Göttingen, Germany;University of Göttingen, Institute for Numerical and Applied Mathematics, Lotzestr. 16-18, 37083 Göttingen, Germany;Technical University of Cluj-Napoca, Department of Mathematics, str. Memorandumului 28, RO-400114 Cluj-Napoca, Romania
Venue:
Journal of Symbolic Computation
Year:
2013

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Abstract

We derive a new deterministic algorithm for the computation of a sparse Legendre expansion f of degree N with M@?N nonzero terms from only 2M function resp. derivative values f^(^j^)(1), j=0,...,2M-1 of this expansion. For this purpose we apply a special annihilating filter method that allows us to separate the computation of the indices of the active Legendre basis polynomials and the evaluation of the corresponding coefficients.