Oversampled Collocation Approximation Method of Functions via Jacobi Frames

Abstract

In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in the uniform norm, especially for differentiable functions. In addition, we show that when the indexes of Jacobi polynomials $α$ and $β$ are larger (for example max$\{α,β\} > 10$), it leads to a divergence behavior on the frame approximation error decay.