Welcome to my home page! How to get in touch Education and Postdoc Position Research Interests Books Conferences Organized Selected Publications Teaching Other Web Sites Check out the Mathematician of the Day Other pictures (including "The Coat")

How to get in touch:

Education and Postdoc Position

• Diplom & Staatsexamen: 1991 University of Stuttgart with Klaus Höllig
• M.A.: 1993 anderbilt University with Larry L. Schumaker
• Ph.D.: 1995 anderbilt University with Larry L. Schumaker
• Visiting Assistant Professor: 1995-1997 orthwestern University with Joe Jerome

Research Interests

• Meshfree Approximation Methods
  
• Radial Basis Functions
• Approximation Theory
• Computer-Aided Geometric Design
• Spline Theory
• Numerical Solution of PDEs

Books

Conferences Organized

15th International Conference on Approximation Theory, May 2016, San Antonio, TX

14th International Conference on Approximation Theory, April 2013, San Antonio, TX

ECCOMAS Thematic Conference on Meshless Methods, July 2007, Porto

Midwest Numerical Analysis Day, June 2007, Chicago

7th International Conference on Computational and Mathematical Methods in Science and Engineering, June 2007, Chicago

Selected Publications

• An Introduction to the Hilbert-Schmidt SVD using Iterated Brownian Bridge Kernels (with Roberto Cavoretto and Mike Mccourt) PDF in Numerical Algorithms.
• Solving support vector machines in reproducing kernel Banach spaces with positive definite functions (with Fred Hickernell and Qi Ye) PDF in ACHA.
• Reproducing kernels of Sobolev spaces via a Green function approach with differential operators & boundary operators (with Qi Ye) PDF in Adv. Comput. Math. 38/4 (2013), 891-921.
  
• Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method (with Igor Cialenco and Qi Ye) Int. J. Comput. Math. 89/18 (2012), 2543-2561 (see also arxiv.org/abs/1108.4213)
• Stable Evaluation of Gaussian RBF Interpolants (with Mike McCourt) PDF in SIAM J. Sci. Comput. 34/2 (2012), A737-A762.
  See also the supporting webpage with downloadable MATLAB code maintained by Mike McCourt.
  
• On Dimension-Independent Rates of Convergence for Function Approximation with Gaussian Kernels (with Fred Hickernell and Henryk Wozniakowski) PDF in SIAM J. Numer. Anal. 50/1 (2012), 247-271.
  
• Multivariate interpolation with increasingly flat radial basis functions of finite smoothness (with Guohui Song, John Riddle, and Fred Hickernell) PDF in Adv. Comp. Math. 36/3 (2012), 485-501.
  
• Positive Definite Kernels: Past, Present and Future PDF Dolomites Research Notes on Approximation, Vol.4 (2011), 21-63.
  In addition, some screen captures of movies mentioned in the paper (as a compressed 7z archive) and "computable documents" in Mathematica's CDF format.
  
• Green's Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions and Splines PDF Approximation Theory XIII: San Antonio 2010, Springer, 2011, 37-63.
  
• Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators (with Qi Ye) PDF in Numerische Mathematik 119/3 (2011), 585-611.
  
• Preconditioning of Radial Basis Function Interpolation Systems via Accelerated Iterated Approximate Moving Least Squares Approximation (with Jack Zhang) PDF in Progress on Meshless Methods, A. J. M. Ferreira, E. J. Kansa, G. E. Fasshauer and V. M. A. Leitao (eds.), Springer, 2009, 57-75.
  
• Tutorial on Meshfree Approximation Methods with Matlab, Slides for 6 Lectures, Dolomites Research Notes on Approximation, Vol. 1, 2008
• On Choosing "Optimal" Shape Parameters for RBF Approximation (with Jack Zhang) PDF in Numerical Algorithms, 45/1-4 (2007), 345-368.
  
• Analysis of Natural Frequencies of Composite Plates by an RBF-Pseudospectral Method (with A. J .M. Ferreira) doi:10.1016/j.compstruct.2005.12.004 Composite Structures 79 (2007), 202-210.
• Scattered Data Approximation of Noisy Data via Iterated Moving Least Squares (with Jack Zhang) PDF in Proceedings of Curve and Surface Fitting: Avignon 2006, T. Lyche, J. L. Merrien and L. L. Schumaker (eds.), Nashboro Press, Brentwood, TN, 2007, 150-159.
  
• Iterated Approximate Moving Least Squares Approximation (with Jack Zhang) PDF in Advances in Meshfree Techniques, V. M. A. Leitao, C. Alves and C. A. Duarte (eds.), Springer, 2007, 221-240.
  
• Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method (with A. J. M. Ferreira) doi:10.1016/j.cma.2006.02.009 Comput. Methods Appl. Mech. Engrg. 196 (2006), 134-146.
• Preface to Radial Basis Functions and Related Multivariate Meshfree Approximation Methods: Theory and Applications, Comp. Math. Applic. 51/8, 2006, xiii--xv.
• RBF Collocation Methods and Pseudospectral Methods PDF .
  
• Recent Results for Moving Least Squares Approximation (with Jack Zhang) PDF in Geometric Modeling and Computing: Seattle 2003, M. L. Lucian and M. Neamtu (eds.), Nashboro Press, Brentwood, TN, 2004, 163-176.
  
• A Parallel Time Stepping Approach Using Meshfree Approximations for Pricing Options with Non-smooth Payoffs (with Abdul Khaliq and Dave Voss) PDF in Proceedings of Third World Congress of the Bachelier Finance Society, Chicago, July 2004.
• Dual Bases and Discrete Reproducing Kernels: A Unified Framework for RBF and MLS Approximation PDF in Journal of Engineering Analysis with Boundary Elements 29 (2005), 313-325.
• Meshfree Methods PDF to appear in Handbook of Theoretical and Computational Nanotechnology, M. Rieth and W. Schommers (eds.), American Scientific Publishers, 2006, 33-97.
• Review of A Course in Approximation Theory by Ward Cheney and Will Light PDF appeared in Mathematical Monthly May 2004, 448-452.
• Using Meshfree Approximation for Multi-Asset American Option Problems (with Abdul Khaliq and Dave Voss) PDF J. Chinese Institute Engineers (Vol.27 No.4) 2004, 563--571.
• Toward Approximate Moving Least Squares Approximation with Irregularly Spaced Centers PDF appeared in Computer Methods in Applied Mechanics & Engineering (193) 2004, 1231-1243.
• Approximate Moving Least-Squares Approximation: A Fast and Accurate Multivariate Approximation Method PDF, DVI, PS-gzipped in Curve and Surface Fitting: Saint-Malo 2002, A. Cohen, J.-L. Merrien, and L. L. Schumaker (eds.), Nashboro Press, 2003, 139-148.
• A Volumetric Integral Radial Basis Function Method for Time-Dependent Partial Differential Equations: I. Formulation (with Ed Kansa, Henry Power and Leevan Ling) PS-gzipped appeared in Journal of Engineering Analysis with Boundary Elements (Vol.28, No.10) 2004, 1191-1206.
• Approximate Moving Least-Squares Approximation for Time-Dependent PDEs PDF, in WCCM V, Fifth World Congress on Computational Mechanics, H. A. Mang, F. G. Rammerstorfer, and J. Eberhardsteiner (eds.), Vienna University of Technology, 2002.
• Approximate Moving Least-Squares Approximation with Compactly Supported Weights DVI, PS-gzipped in Lecture Notes in Computer Science and Engineering Vol.26: Meshfree Methods for Partial Differential Equations, M. Griebel and M. A. Schweitzer (eds.), Springer Verlag, 2002, 105-116.
• Matrix-free Multilevel Moving Least-Squares Methods in Approximation Theory X: Wavelets, Splines, and Applications, C. K. Chui, L. L. Schumaker, and J. Stöckler (eds.), Vanderbilt University Press, 2002, 271-281. DVI (without figures), PS-gzipped
• Newton Iteration with Multiquadrics for the Solution of Nonlinear PDEs appeared in Comput. Math. Applic. (43) 2002, 423-438. DVI (without figures), PS-gzipped
• Nonsymmetric Multilevel RBF Collocation within an Operator Newton Framework for Nonlinear PDEs, appeared in Trends in Approximation Theory, K. Kopotun, T. Lyche, and M. Neamtu (eds.), Vanderbilt University Press, 2001, 103-112. DVI (without figures), PS-gzipped
• Newton Iteration for Partial Differential Equations and the Approximation of the Identity (with Chuck Gartland and Joe Jerome) appeared in Numerical Algorithms (25) 2000, 181-195. DVI (without figures), PS-gzipped
• Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and Smoothing (with Chuck Gartland and Joe Jerome) appeared in J. Comp. Appl. Math. (119) 2000, 161-183. DVI (without figures), PS-gzipped
• On the Numerical Solution of Differential Equations with Radial Basis Functions appeared in Boundary Element Technology XIII, C. S. Chen, C. A. Brebbia, and D. W. Pepper (eds.), WIT Press, 1999, 291-300. DVI (without figures), PS-gzipped
• Solving Differential Equations with Radial Basis Functions: Multilevel Methods and Smoothing appeared in Adv. in Comp. Math. (11) 1999, 139-159. DVI (without figures), PS-gzipped
• On Smoothing for Multilevel Approximation with Radial Basis Functions appeared in Approximation Theory XI, Vol.II: Computational Aspects, Charles K. Chui, and L. L. Schumaker (eds.), Vanderbilt University Press, 1999, 55-62. DVI, PS-gzipped
• Scattered Data Fitting on the Sphere (with Larry Schumaker) appeared in Mathematical Methods for Curves and Surfaces II, M. Daehlen, T. Lyche, and L. L. Schumaker (eds.), Vanderbilt University Press, 1998, 117-166. DVI, PS-gzipped
• Multistep Approximation Algorithms: Improved Convergence Rates through Postconditioning with Smoothing Kernels (with Joe Jerome) appeared in Adv. in Comp. Math. (10) 1999, 1-27. DVI (without figures), PS-gzipped
• Solving Partial Differential Equations by Collocation with Radial Basis Functions appeared in Surface Fitting and Multiresolution Methods, A. Le Mehaute, C. Rabut, and L. L. Schumaker (eds.), Vanderbilt University Press, 1997, 131-138. DVI (without figures), PS-gzipped
• Minimal Energy Surfaces using Parametric Splines (with Larry Schumaker) appeared in Computer-Aided Geometric Design (13) 1996, 45-79. DVI (without figures)
• Adaptive Least Squares Fitting with Radial Basis Functions on the Sphere appeared in Mathematical Methods for Curves and Surfaces M. Daehlen, T. Lyche, and L. L. Schumaker (eds.), Vanderbilt University Press, 1995, 141-150. DVI (without figures), PS-gzipped
• Hermite Interpolation with Radial Basis Functions on Spheres appeared in Adv. in Comp. Math. (10) 1999, 81-96. DVI, PS-gzipped
• References for Radial Basis Functions (last updated 12/19/2003) PDF

Teaching

• Mathematica Labs for MATH 151 and MATH 152
• Interprofessional Project (IPRO 330) "Creating a Dynamic and Contemporary Math and Science Fair Project Bank for Chicago Public Schools" (Spring 09)
• 100 Introduction to the Profession (Fall 12)
• 152 Calculus II (Fall 03)
• 161 Honors Calculus I (Fall 98)
• 162 Honors Calculus II (Fall 01, cancelled)
• 251 Multivariate and Vector Calculus (Spring 04)
• 252 Introduction to Differential Equations (Fall 01)
• 333 Matrix Algebra and Complex Variables (Spring 00)
• 350 Introduction to Computational Mathematics (Spring 11)
• 461 Fourier Series and Boundary Value Problems (Fall 15)
• 471 Numerical Methods I (Fall 98)
• 472 Numerical Methods for Differential Equations (Fall 05)
• 473 Numerical Linear Algebra (Fall 04)
• 477 Numerical Linear Algebra (Fall 06)
• 478 Numerical Methods for Differential Equations (Spring 07)
• 532 Linear Algebra (Spring 15)
• 577 Computational Mathematics I (Fall 06)
• 578 Computational Mathematics II (Spring 07)
• 590 Meshfree Methods (Fall 2014)
• 603 Multivariate Meshfree Approximation (Fall 2003)

Other Web Sites

• Numerical Analysis in the Midwest
• NA-Net
• AT-Net
• SIAM
• Guide to Available Mathematical Software
• NIST Digital Library of Mathematical Functions
• MacTutor History of Mathematics Archive
• Chicago Symphony Orchestra
• Chicago Bulls
• Chicago
• Naperville

Last updated: December 21, 2015