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TITLE: Residual Updating Algorithms for Kernel Interpolation
SPEAKER: Greg Fasshauer
ABSTRACT:
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
