Fractal-classic interpolants
Volume 84 / 2009
Abstract
The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional condition of proximity to another interpolant leads to a problem of convex optimization whose solution is a fractal element with mixing properties. This procedure may be applied to the reduction of the regularity order of traditional approximants and for the computation of models with rich geometric structure.
