An analysis of (0,1;0) interpolation based on roots of Pál-type interpolatory polynomials

Abstract

The objective of this paper is to investigate an interpolation process based on the roots of the polynomial  and it′s subject to an additional conditional Point . Specifically, we consider two sets of nodes: representing the roots of  and   corresponding to the roots of . Our study focuses on eThe objective of this paper is to investigate an interpolation process based on the roots of the polynomial  and it′s subject to an additional conditional Point . Specifically, we consider two sets of nodes: representing the roots of  and   corresponding to the roots of . Our study focuses on establishing the existence and uniqueness of the interpolatory polynomial, deriving its explicit representation, and analysing its order of convergencestablishing the existence and uniqueness of the interpolatory polynomial, deriving its explicit representation, and analysing its order of convergence