Non-uniform WENO-based quasi-interpolating splines from the Bernstein–Bézier representation and applications

Abstract

In this paper, we propose a family of C1 non-uniform cubic quasi-interpolation schemes. The construction used here is mainly based on directly establishing the BB-coefficients by a suitable combination of the data values. These combinations generate masks for each of the BB-coefficients. These masks can contain free parameters, which allow us to write a quasiinterpolation schemes defined from a large stencil as a non-negative convex combination of others defined from sub-stencils of small sizes, which coincide with the concept of WENO, which we will use the deal with non-smooth data, or data with jumps. We consider an application of the proposed technique for real measured data related to memristors fabricated with hafnium oxide as a dielectric.