论文标题
通过雅各比帧的稳定函数的稳定近似
Stable approximation of functions from equispaced samples via Jacobi frames
论文作者
论文摘要
在本文中，我们研究了雅各比框架的近似，并带有稳定的样品，并得出了误差估计。我们从数值上观察到，随着扩展域参数$γ$的增加，近似精度逐渐降低，尤其是对于可区分的功能而言。此外，我们表明，当Jacobi多项式$α$和$β$的索引更大（例如$ \ max \ {α，β\}> 10 $）时，它会导致帧近似误差衰减的差异行为。
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 $γ$ 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.
