A simple method for smoothing functions and compressing Hermite data
Consider a function \(f:[a,b] \to \mathbb R\) and a grid \(a = x_0 < x_1 < \cdots < x_n = b\). Assume that \(f \in C^k[x_i, x_{i+1}]\) for all \(i\) but \(f\) is only \(k_i\) times differentiable at the break point \(x_i\) (where \(k_i < k\)). The goal of the paper is to construct a function \(f_k \in C^k[a,b]\) that approximates \(f\), thus smoothing \(f\) at the points \(x_i\). This is achieved by a method based on a small modification of the concept of Bernstein polynomials. As an application, interpolatory splines in the Hermite sense can be computed in a recursive way, leading to a concept closely related to a multiresolution analysis. This allows to perform a data compression.
scientific article; zbMATH DE number 2170077