Hermite Lagrange Interpolation on the Unit Circle

In this paper, we consider explicit representations and convergence of Hermite- Lagrange Interpolation on two disjoint sets of nodes, which are obtained by projecting vertically the zeros of (1- x2) Pn (? ,? ) (x) and Pn ( ? ,? )(x)  respectively on the unit circle, where Pn( ?, ?)  (x) stands for Jacobi polynomials

(R1521) On Weighted Lacunary Interpolation

In this paper, we considered the non-uniformly distributed zeros on the unit circle, which are obtained by projecting vertically the zeros of the derivative of Legendre polynomial together with x=1 and x=-1 onto the unit circle. We prescribed the function on the above said nodes, while its second derivative at all nodes except at x=1 and x=-1 with suitable weight function and obtained the existence, explicit forms and establish a convergence theorem for such interpolatory polynomial. We call such interpolation as weighted Lacunary interpolation on the unit circle

(R2054) Convergence of Lagrange-Hermite Interpolation using Non-uniform Nodes on the Unit Circle

In this study, we investigated a Lagrange-Hermite interpolation problem by taking into account the collection of non-uniformly distributed nodes on the unit circle. These nodes are created by vertically projecting the unit circle’s boundary points on the real line and the Jacobi polynomial’s zeros onto the unit circle. The two main accomplishments of this article are the explicit representation of the interpolatory polynomial and the proof of the convergence theorem. The field of approximation theory entertains the results proved