Quasi-interpolation with radial basis functions

Abstract: \\
As an alternative to interpolation in high dimensions using the universal and successful method of radial basis functions, there is the method of quasi-interpolation that also works in many dimensions and with all known classes of radial basis functions such as Gauss kernels and multiquadrics. In this talk we describe the approach of quasi-interpolation, show the existence of quasi-Lagrange functions and study in detail their convergence behaviour to approximands that are in suitable function spaces.