Multipoint polynomials and basis for scattered data interpolation

Interpolation problems arise in many areas where there is a need to construct a continuous surface from irregularly spaced data points. These areas include cartography, geophysics, data mining, engineering, meteorology, landscape ecology, computer graphics, and scientific visualization. Among the number of solutions to this problem, the choice of interpolation technique depends on the distribution of points in the data set, application domain, approximating function, or the method that is prevalent in the discipline. Shepard's interpolation method, based on a weighted average of values at the data points, usually creates good approximations. Over the years several variations of the original Shepard method have been proposed in order to increase the accuracy of approximation, to improve the efficiency, or even to solve specific interpolation problems. In this talk we summarize results that we obtained on this topic in the latest years and point out challenges for future research.

Francesco Dell'Accio is an Associate Professor in the Department of Mathematics and Informatics at the University of Calabria. He received a Ph.D. in Mathematical Analysis from the Steklov Mathematical Institute of the Russian Academy of Sciences (Moscow) under the supervision of Anatoly G. Vitushkin. Professor Dell'Accio's primary research interest is in theory of approximation. In particular, he has been working on mixed polynomial interpolation and regression, scattered data approximation and interpolation, polynomial approximation of smooth functions by means of boundary values, boundary type quadrature formulas. He collaborated in research on applications of Mathematics and in particular on Physics of Fluvial Networks and Statistical Analysis of Non-Linear Processes.

During the Ph.D. studies at the Steklov Mathematical Institute he worked on Complex Analysis and in particular on topological approaches to the Jacobian Conjecture. He is an associate Editor of the Dolomites Research Notes on Approximation.