Residual Updating Algorithms for Kernel Interpolation

Event Details
  • Date/Time:
    • Wednesday April 21, 2010
      10:00 am - 11:00 am
  • Location: IC 213
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Summary Sentence: Residual Updating Algorithms for Kernel Interpolation

Full Summary: Residual Updating Algorithms for Kernel Interpolation

TITLE: Residual Updating Algorithms for Kernel Interpolation

SPEAKER: Greg Fasshauer


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

Additional Information

In Campus Calendar

H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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  • Created By: Anita Race
  • Workflow Status: Published
  • Created On: Apr 19, 2010 - 3:47am
  • Last Updated: Oct 7, 2016 - 9:51pm