Rational Interpolation with Parameters Based on Chebyshev Nodes

Abstract

A type of rational interpolation operator (RIO) with parameter $\lambda$ is studied in this paper. We give the specific construction of RIO based on Chebyshev nodes of the fourth kind, and calculate the approximation order of the RIO to functions when $1<\lambda<2$ and $\lambda>2$ respectively. Furthermore, we analyze the relation between the parameter $\lambda$ and the approximate error, while the latter is between the operator and the function. By selecting the sampling function and adjusting the parameter, the theoretical results are visualized and verified from the images and error data tables.