Oversampled Collocation Approximation Method of Functions via Jacobi Frames (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, we study the Jacobi frame approximation with equispacedsamples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $γ$ increases in theuniform norm, especially for differentiable functions. In addition, we show that whenthe indexes of Jacobi polynomials $α$ and $β$ are larger (for example max$\{α,β\} > 10$), itleads to a divergence behavior on the frame approximation error decay.