PhD research topic - Biancamaria Della Vecchia
Research areas
Approximation theory, positive operators
Keywords
Bernstein-type operators, Shepard operators
Research topics
Literature on polynomial and rational approximation is very wide. In particular Bernstein-type operators are powerful tools to approximate functions and heriditate many of its properties by very simple mathematical structures. Thanks to this modeling behavior Bernstein-type operators are nowadays subject of research to get faster converging generalizations and to apply them in various areas, as for example in CAGD. On the other hand rational operators like Shepard-type operators achieve approximation results not possible by polynomials and are widely used in several applicative problems involving scattered data interpolation. In the last years research on such operators is aimed at investigating extensions of Shepard-type operators reaching better approximation error estimates or more performing techniques by such operators in various contexts like CAGD, data fitting, image processing, denoising problems. Knowledge of MATLAB is required to investigate.
Bibliography
[1] K. Anjyo, J. P. Lewis, F. Pighin, Scattered data interpolation for Computer graphics, Siggraph 1-69, 2014
[2] S. Gal , Global smoothness and shape preserving interpolation by classical operators, G. Anastassiou (Ed.) Springer 2005