Professor and Department Head, Applied Mathematics and Statistics
- Diplom in Mathematics (1991) University of Stuttgart
- Staatsexamen in Mathematics and English (1991) University of Stuttgart
- M.A. in Mathematics (1993) Vanderbilt University
- Ph.D. in Mathematics (1995) Vanderbilt University
- Meshfree Approximation Methods
- Radial Basis Functions
- Approximation Theory
- Numerical Solution of PDEs
- Spline Theory
- Computer-Aided Geometric Design
- (with M. J. McCourt) Kernel-based Approximation Methods using MATLAB, Interdisciplinary Mathematical Sciences Vol.9, World Scientific Publishers, Singapore, 2015.
- (with G. Ala, E. Francomano, S. Ganci and M. McCourt) The method of fundamental solutions in solving coupled boundary value problems for M/EEG, SIAM J. Sci. Comput. 37/4 (2015), B570-B590.
- (with R. Cavoretto and M. McCourt) An introduction to the Hilbert-Schmidt SVD using iterated Brownian bridge kernels, Numerical Algorithms 86 (2015), 393-422.
- (with F. Hickernell and Q. Ye) Solving support vector machines in reproducing kernel Banach spaces with positive definite functions, Appl. Comput. Harmon. Anal. 38/1 (2015), 115-139.
- (with Q. Ye), Reproducing kernels of Sobolev spaces via a Green function approach with differential operators & boundary operators, Adv. Comp. Math. 38/4 (2013), 891-921.
- (with I. Cialenco and Q. Ye) Approximation of stochastic partial differential equations by a kernel-based collocation method, Int. J. Comput. Math. 89/18 (2012), 2543-2561.
- (with M. J. McCourt) Stable evaluation of Gaussian radial basis function interpolants, SIAM J. Sci. Comput. 34/2 (2012), A737-A762.
- (with F. J. Hickernell and H. Wozniakowski) On dimension-independent rates of convergence for function approximation with Gaussian kernels, SIAM J. Numer. Anal. 50/1 (2012), 247-271.
- (with G. Song, J. Riddle, and F. J. Hickernell), Multivariate interpolation with increasingly flat radial basis functions of finite smoothness, Adv. Comp. Math. 36/3 (2012), 485-501.