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
