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Volume 16, Issue 3
Oversampled Collocation Approximation Method of Functions via Jacobi Frames

Xianru Chen & Li Lin

Adv. Appl. Math. Mech., 16 (2024), pp. 569-588.

Published online: 2024-02

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  • 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.

  • AMS Subject Headings

41A10, 41A25, 41A17

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-569, author = {Chen , Xianru and Lin , Li}, title = {Oversampled Collocation Approximation Method of Functions via Jacobi Frames}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {3}, pages = {569--588}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0071}, url = {http://global-sci.org/intro/article_detail/aamm/22929.html} }
TY - JOUR T1 - Oversampled Collocation Approximation Method of Functions via Jacobi Frames AU - Chen , Xianru AU - Lin , Li JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 569 EP - 588 PY - 2024 DA - 2024/02 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2022-0071 UR - https://global-sci.org/intro/article_detail/aamm/22929.html KW - Jacobi polynomial, frame, oversampled, collocation, equispaced sample. AB -

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.

Chen , Xianru and Lin , Li. (2024). Oversampled Collocation Approximation Method of Functions via Jacobi Frames. Advances in Applied Mathematics and Mechanics. 16 (3). 569-588. doi:10.4208/aamm.OA-2022-0071
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