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

In this paper, we introduce and analyze the behavior of a nonlinear subdivision operator called PPH, which comes from its associated PPH reconstruction on nonuniform grids. The acronym stands for Piecewise Polynomial Harmonic, since is built by using piecewise polynomials defined means an adaption based use weighted Harmonic mean. novelty work lies in generalization already existing scheme to case. We define corresponding study some important issues related schemes such as convergence, smoothness limit function, preservation convexity. order obtain general results, consider σ quasi-uniform also perform numerical experiments reinforce theoretical results.