In this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

中文翻译：

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重心长齿插值和伪谱微分

在本文中，我们将提供基于重心观点的长插值和伪谱微分的进一步说明。推导了重心扁长插值和伪谱微分的收敛速度。此外，我们提出了一种新的预处理器，该预处理器导致了条件良好的曲线搭配方案。数值例子表明了该新方法的高精度。我们采用这种方法来解决二阶边值问题和亥姆霍兹问题。