TITLE: Residual Updating Algorithms for Kernel InterpolationSPEAKER: Greg FasshauerABSTRACT:I will first present two scattered data approximation methods from a numerical analysis point of view: radial basis function or kernel interpolation and moving least squares approximation. Then I will introduce the idea of approximate moving least squares approximation and connect all three methods via a residual updating algorithm. In parallel I will attempt to point out connections to an analogous set of methods (kriging, local polynomial regression and higher-order kernels for density estimation) in statistics. The idea of residual updating will be illuminated both from a more analytical perspective and at the numerical linear algebra level where we have rediscovered an old algorithm due to Riley [1]. [1] J.D. Riley. Solving systems of linear equations with a positive definite, symmetric, but possibly ill-conditioned matrix. Mathematical Tables and Other Aids to Computation 9/51 (1955), 96–101. Brief bio: Greg Fasshauer Professor, Associate Chair and Director of Undergraduate Studies Illinois Institute of Technology Department of Applied Mathematics Chicago, IL 60616 Education and Positions * Since 1997: Assistant, associate and full professor, Department of Applied Mathematics, IIT * Ralph P. Boas Visiting Assistant Professor: Department of Mathematics, Northwestern University (1995-1997) * Ph.D. (Mathematics): Vanderbilt University with Larry L. Schumaker (1995) * M.A. (Mathematics): Vanderbilt University with Larry L. Schumaker (1993) * Diplom (Mathematics) & Staatsexamen (Mathematics and English): University of Stuttgart with Klaus Höllig (1991) Research Interests (currently supported by NSF) * Meshfree approximation methods for multivariate approximation and their application * Radial basis functions and positive definite kernels * Approximation theory * Computer-aided geometric design * Spline theory * Numerical solution of PDEs Books and 40+ papers * Meshfree Approximation Methods with MATLAB Interdisciplinary Mathematical Sciences - Vol. 6 World Scientific Publishers, Singapore, 2007 * Progress on Meshless Methods (edited with A.J.M. Ferreira, E.J. Kansa, and V.M.A. Leitão) Computational Methods in Applied Sciences, Vol. 11 Springer, Berlin, 2009