Recursive evaluation procedures based on spherical linear interpolation and stationary subdivision algorithms based on geodesic midpoint averaging are used to construct the analogues on spheres of arbitrary dimension of Lagrange and Hermite interpolation and Bezier and B-spline approximation.

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness cond...

In this paper we propose a learning based iterative numerical method for computing a rootξ of a non-linear equation of the form f(x) = 0 in the interval [a,b]. Lag based method through Hermite interpolation modeled root discovery approach is developed and demonstrated in this paper. The new method has been tested for a series of functions considered by several researchers. The numerical experim...