Sparse sums with bases of Chebyshev polynomials of the third and fourth kind

Abstract

We derive a generalization for the reconstruction of M -sparse sums in Chebyshev bases of the third and fourth kind. This work is used for a polynomial with Chebyshev sparsity and samples on a Chebyshev grid of [−1, 1] .Further, fundamental reconstruction algorithms can be a way for getting M-sparse expansions of Chebyshev polynomials of the third and fourth kind. The numerical results for these algorithms are designed to compare the time effects of doing them.