Representation of sparse Legendre expansions
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. (C) 2012 Elsevier B.V. All rights reserved.
annihilating filters legendre polynomials sparse polynomial expansions nonlinear approximation