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