The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids

In this paper, we define a translation operator in a general form to allow for the application of the weighted harmonic mean in different applications. We outline the main steps to follow to define adapted methods using this tool. We give a practical example by improving the behavior of a nonlinear reconstruction operator defined in nonuniform grids, which was initially meant to work well with strictly convex data. With this improvement, the reconstruction can be now applied to data coming from smooth functions, retaining the expected maximum approximation order even around the inflection point areas, and maintaining convexity properties of the initial data. This adaptation can be carried out for general nonuniform grids, although to get the theoretical results about the approximation order, we require to work with quasi-uniform grids. We check the theoretical results through some numerical experiments

Sobre algunas técnicas de aproximación usadas en diseño asistido por computador

Las conclusiones de este TFG indican que los nuevos esquemas de subdivisión no lineal que se han presentado tienen las siguientes propiedades:1.son esquemas de interpolación ternarios , que convergen hacia funciones de regularidad superior a uno. 2.si los datos iniciales provienen de discretizar una función discontinua, las funciones límite no oscilan, a diferencia de lo que ocurre en los clásicos esquemas interpolatorios lineales. 3.las transformadas multiresolución asociadas son estables. Y constituyen la primera familia de esquemas que comparten simultáneamente esas propiedades tan deseables.Escuela Técnica Superior de Ingeniería de TelecomunicaciónUniversidad Politécnica de Cartagen