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

作者：Shams Solary Maryam^*

来源：Turkish Journal of Mathematics, 2016, 40(2): 250-271.

DOI：10.3906/mat-1411-56

• Sparse interpolation
• Chebyshev polynomial
• Prony method
• eigenvalue problem
• Toeplitz-plus-Hankel matrix
• SVD
• QR decomposition

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.

• 出版日期2016