Adv. Appl. Math. Mech., 16 (2024), pp. 569-588.
Published online: 2024-02
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0071}, url = {http://global-sci.org/intro/article_detail/aamm/22929.html} }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.