On rational Hermite-Fej\'{e}r interpolation

Abstract

This article focuses on the study of Hermite-Fej\'{e}r interpolation in a rational space. We constructed the rational functions with poles $\{-1,1\}$ satisfying the conditions of the Hermite-Fej\'{e}r interpolation on the nodes of the orthogonal Jacobi polynomial. The objective is to determine the quantitative estimate of the corresponding interpolatory function. Further, some numerical simulations are performed to demonstrate the effectiveness of the theory of the research work.