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Gregory Fasshauer

Gregory Fasshauer, Ph.D.

Gregory Fasshauer
Professor of Applied Mathematics
Associate Chair and Director of Undergraduate Studies for the Department of Applied Mathematics

Phone: 

312.567.3149

Fax: 

312.567.3135

Office: 

Engineering 1, Room 208A

Office Hours: 

MW 2:00 - 3:00 pm
and by appointment

Education 

Ph.D. in Mathematics - Vanderbilt University (1995)
MA in Mathematics - Vanderbilt University (1993)
Diploma & Staatsexamen in Mathematics and English - University of Stuttgart (1991)

Research & Accomplishments 

Meshfree methods for multivariate approximation (radial basis functions, moving least squares and related methods), Applications of meshfree methods (surface and solid model compression, image compression, options pricing, vibration analysis of composite beams and plates, gas-dynamics), Numerical analysis (solution of differential and integral equations, Nash iteration, multilevel algorithms, fast summation methods, meshfree pseudospectral methods, parallel computing), Approximation theory (approximation on spheres, approximate approximation), Computer-aided geometric design (minimal energy surfaces, geometric continuity), Spline theory (approximation with multivariate splines, dimensions of multivariate spline spaces).

Awards 

2012 - Distinguished Teaching Fellow, College of Science and Letters

2008 - AMS Menger Prize Committee

2007 - Dean's Excellence Award for Teaching, College of Science and Letters, IIT.

2003 - Fellow of Wessex Institute of Technology, Great Britain.

1995 - Bjarni Jonsson Prize for Research, Vanderbilt University.

Books 

 Approximation Theory XIV: San Antonio 2013 (edited with Larry Schumaker), Proceedings in Mathematics & Statistics, Vol. 83, Springer, New York, 2014

Progress on Meshless Methods (with A.J.M. Ferreira, E.J. Kansa and V.M.A. Leitao), Springer, New York, 2008

Meshfree Approximation Methods with MATLAB, World Scientific, 2007

Publications 

SELECTED PUBLICATIONS

 An Introduction to the Hilbert-Schmidt SVD using Iterated Brownian Bridge Kernels, with R. Cavoretto and M. McCourt, Numerical Algorithms, DOI: 10.1007/s11075-014-9850-z.

 Solving support vector machines in reproducing kernel Banach spaces with positive definite functions, with Q. Ye and F. Hickernell, Applied & Computational Harmonic Analysis, DOI: 10.1016/j.acha.2014.03.007.

Reproducing kernels of Sobolev spaces via a Green function approach with differential operators & boundary operators, with Q. Ye , Adv. Comp. Math. 38/4 (2013), 891-921.

 Approximation of stochastic partial differential equations by a kernel-based collocation method, with I. Cialenco and Q. Ye, Int. J. Comput. Math. 89/18 (2012), 2543-2561.

On dimension-independent rates of convergence for function approximation with Gaussian kernels, with F.J. Hickernell and H. Wozniakowski, SIAM J. Numer. Anal. 50/1 (2012), 247-271.

Stable evaluation of Gaussian radial basis function interpolants, with M.J. McCourt, SIAM J. Sci. Comput. 34/2 (2012), A737-A762.

Positive definite kernels: past, present, future, Dolomites Research Notes on Approximation 4 (2011), 21-63.

Reproducing kernels of generalized Sobolev spaces via a Green function apporach with distributional operators, with Q. Ye, Numer. Math 119 (2011), 585-611.

On choosing "optimal" shape parameters for RBF approximation, with J.G. Zhang, Numerical Algorithms 45 (2007), 345-368.

Newton iteration with multiquadrics for the solution of nonlinear PDEs, Comput. Math. Applic. 43 (2002), 423—438.

Multistep approximation algorithms: improved convergence rates through postconditioning with smoothing kernels, with Joe Jerome, Adv. Comput. Math. 10 (1999), 1—27.

Scattered data fitting on the sphere, with LL Schumaker, M. Daehlen, and T. Lyche, in Mathematical Methods for Curves and Surfaces II, Vanderbilt University Press, pg. 117-166, 1998.

Solving partial differential equations by collocation with radial basis functions, with A Le Mehaute, C. Rabut, and LL Schumaker, in Surface Fitting and Multiresolution Methods, Vanderbilt University Press, pg. 131-138, 1997.

Professional Societies