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Fakultät für Mathematik
Daniel Potts, Manfred Tasche: Reconstruction of sparse Legendre and Gegenbauer expansions

Daniel Potts, Manfred Tasche: Reconstruction of sparse Legendre and Gegenbauer expansions


Author(s):
Daniel Potts
Manfred Tasche
Title:
Daniel Potts, Manfred Tasche: Reconstruction of sparse Legendre and Gegenbauer expansions
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 12, 2013
Mathematics Subject Classification:
65D05 [Interpolation ]
33C45 [Orthogonal polynomials and functions of hypergeometric type ]
41A45 [Approximation by arbitrary linear expressions ]
65F15 [Eigenvalues, eigenvectors ]
Abstract:
We present a new deterministic algorithm for the reconstruction of sparse Legendre expansions from a small number of given samples. Using asymptotic properties of Legendre polynomials, this reconstruction is based on Prony--like methods. Furthermore we show that the suggested method can be extended to the reconstruction of sparse Gegenbauer expansions of low positive order.
Keywords:
Legendre polynomials, sparse Legendre expansions, Gegenbauer polynomials, ultraspherical polynomials, sparse Gegenbauer expansions, sparse recovering, sparse Legendre interpolation, sparse Gegenbauer interpolation, asymptotic formula, Prony--like method
Language:
English
Publication time:
07/2013

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