Analysis of a New Nonlinear Interpolatory Scheme on Quasi-Uniform Grids

In this paper, we tend to introduce and analyze the behavior of a nonlinear subdivision operator referred to as PPH, that comes from its associated PPH nonlinear reconstruction operator on inhomogeneous grids. The descriptor PPH stands for Piecewise Polynomial Harmonic, since the reconstruction is constructed by victimisation piecewise polynomials outlined by means that of associate degree adaption supported the employment of the weighted mean value. The novelty of this work lies within the generalization of the already existing PPH subdivision theme to the inhomogeneous case. we tend to outline the corresponding subdivision theme and study some vital problems associated with subdivision schemes like convergence, smoothness of the limit perform, and preservation of convexity. so as to get general results, we tend to think about think about quasi-uniform grids. we tend to conjointly perform some numerical experiments to strengthen the theoretical results.