7th International Conference on Computational and Mathematical Methods in Science and Engineering, June 2007, Chicago
Selected Publications
Compact Matern Kernels and Piecewise Polynomial Splines Viewed From a Hilbert-Schmidt Perspective
(with Roberto Cavoretto and Mike Mccourt)
PDF, to appear in Numerical Algorithms.
Green's Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions and SplinesPDF Approximation Theory XIII: San Antonio 2010, Springer, 2011, 37-63.
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.
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.
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.
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.
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.2005.12.004Composite 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.2006.02.009Comput. Methods Appl. Mech. Engrg. 196 (2006), 134-146.
RBF Collocation Methods and Pseudospectral MethodsPDF .
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 ApproximationPDF
in Journal of Engineering Analysis
with Boundary Elements 29 (2005), 313-325.
Meshfree MethodsPDF 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 LightPDF
appeared in Mathematical Monthly May 2004, 448-452.
Using Meshfree Approximation for Multi-Asset American
Option Problems (with Abdul Khaliq and Dave Voss) PDFJ. Chinese Institute
Engineers (Vol.27
No.4) 2004, 563--571.
Toward Approximate Moving Least Squares Approximation with
Irregularly Spaced CentersPDF
appeared in Computer Methods in Applied Mechanics & Engineering
(193) 2004, 1231-1243.
Approximate Moving Least-Squares Approximation: A Fast and
Accurate Multivariate Approximation MethodPDF,
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 PDEsPDF, 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 WeightsDVI, 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