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.
Sparse interpolation, Chebyshev polynomial, Prony method, eigenvalue problem, Toeplitz-plus-Hankel matrix, SVD, QR decomposition
SOLARY, MARYAM SHAMS
"Sparse sums with bases of Chebyshev polynomials of the third and fourth kind,"
Turkish Journal of Mathematics: Vol. 40:
2, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/3