Reconstruction of sparse Legendre and Gegenbauer expansions

Recently the reconstruction of sparse trigonometric polynomials has attained much attention. There exist recovery methods based on random sampling related to compressed sensing (see e.g. [17, 10, 5, 4] and the references therein) and methods based on deterministic sampling related to Prony–like methods (see e.g. [15] and the references therein). Both methods are already generalized to other polynomial systems. Rauhut and Ward [18] presented a recovery method of a polynomial of degree at most N − 1 given in Legendre expansion with M nonzero terms, where O(M (logN)4) random samples are ∗[email protected], Chemnitz University of Technology, Department of Mathematics, D–09107 Chemnitz, Germany ‡[email protected], University of Rostock, Institute of Mathematics, D–18051 Rostock, Germany