M.S. Jilin University, Changchun, P.R. China, 1983
PROFESSIONAL EXPERIENCES
Associate Professor, Department of Mathematical Scineces,
University of Nevada, Las Vegas, 1998 - present
Assistant Professor, Department of Mathematical Scineces,
University of Nevada, Las Vegas, 1992 - 1998.
Research Associate, Department of Mathematics and Departmnet of
Aerospace Engineering, University of
Texas A&M University, 1991 - 1992.
Assistant Lecturer, Department of Mathematics, Texas
A&M University, 1990-1991.
RESEARCH INTERESTS
My research interests lie in approximation by radial basis functions
and neural networks, and in applied analysis and systems theory.
TEACHING (Fall 2008)
Office Hours
SELECTED PUBLICATIONS
Radial basis approximation and its application to biharmonic equation,
Advances in Computational Mathematics, in press.
Approximation of potential integral by radial bases for solutions
of Helmholtz equations, Advances in Computational Mathematics, in press.
Rate of convergence of the method of fundamental solutions and
hyperinterpolation for modified Hemholtz equations on the unit ball,
Advances in Computational Mathematics, 29 (2008), 393-413.
Convergence of the method of fundamental solutions for Poisson's
equations on the unit sphere, Advances in Computational Mathematics,
28 (2008), 269-292.
On the methods of fundamental solutions in R2, Journal of Information
and Computational Sciences, 4:2 (2007), 567-586.
Rate of approximation by the method of fundamental solutions for
Laplace equation on the unit sphere, Journal of Information and
Computational Sciences, Vol. 3, No. 2 (2006), 245-254.
On solving boundary value problems of modified Helmholtz equations
by plane wave functions, Journal of Computational and Applied Mathematics,
195 (2006), 66-82.
On convergence of the method of fundamental solutions for solving
the Dirichlet problem of Poisson's equation, Advances in Computational
Mathematics, Vol. 23 (2005), 265-277.
Convergence of the method of fundamental solutions for solving
the boundary value problem of modified Helmholtz equation, Applied
Mathematics and Computation, Vol. 159 (2004), 113-125.
A mesh free method using hyperinterpolation and Fast Fourier transform
for solving differential equations, (with C.S. Chen), Journal of
Engineering Analysis with Boundary Elements, 28 (2004), 1253-1260.
Trefftz methods for time dependent partial differential equations,
with H.A. Cho, M.A. Golberg, and A.S. Muleshkov), the journal of Computers,
Materials, and Continua, Vol. 1, No. 1, (2004), 1-37
On the continuity of methods of fundamental solutions, proceeding
of 2004 International Conference on Computational & Experimental
Engineering and Sciences, CD-rom, 2004.
Computation of particular solutions by hyperinterpolation and
Fast Fourier transform, (with C.S. Chen and M.A. Golberg), Proceedings
of 2003 International Conference on Computational & Experimental
Engineering and Sciences, CD-rom 2003.
On the convergence of the dual reciprocity method for Poisson's
equation, (with M.A. Golberg), Transformation of Domain Effects to
the Boundary, Y.F. Rashed and C.A. Brebbia, ed., 2003, 227-251.
Interpolation by ridge polynomials and its application in neural
networks, Journal of Computational and Applied Mathematics, 144
(2002), 197-209.
Computational test of approximation of functions and their derivatives
by radial basisfunctions, (with C.H. Ho and C.S. Chen), Journal of Neural,
Parallel and Scientific Computation, 10 (2002), 25-46.
Training multilayer perceptrons via minimization of sum of ridge functions,
with W. Wu and G. Feng), Advances in Computational Mathematics, 17 (2002),
331-347.
On methods for solving the Dirichlet problem for Poisson's equation, (with
M.A. Golberg), Boundary Elements XXIV, Brebbia, Tadeu, and Popov, ed., 2002,
87-96.
Subspace computations in statistics using the singular value decomposition
- a sampler, (with G. Miel, M. Marcozzi, I. Farnham, and A.K. Singh), Hawaii
Int. Conf. Stat. Related Fields, CD-rom 2002.
Training multilayer perceptrons via interpolation by superpositions of
an activation function, Proceedings of the international conference on mathematics
and engineering techniques in medicine and biological sciences, F.
Valafar, ed. 2001, 19-24.
Construction of radial basis functions for approximation, (with C.H. Ho
and C.S. Chen), Proceedings of 24th international conference on the advances
in computational engineering and sciences, S.N. Atluri, T. Nishioka, and M.
Kikuchi, ed., Tech science press, CD-rom, 2001.
Approximation by radial bases and neural networks, (with C.A. Micchelli),
Numerical Algorithms, 25 (2000), 241-262.
A simple remark on the order of approximation by compactly
supported radial basis functions and related networks, in Boundary
Element Technology XIII, C.S. Chen, C.A. Brebbia, and D.W. Pepper, eds,
WIT Press, 1999, 335-343.
On simultaneous approximations by radial basis function
neural networks", Applied Mathematics and Computation,
95 (1998), 75-89.
Simultaneous approximation of multivariate functions and their
derivatives by neural networks with one hidden layer,
International Journal of Neurocomputing, 12 (1996), 327-343.
L_1 approximation of a certain class of infinite dimensional
systems in time-domain, IEEE Transactions on Circuits and Systems,
Vol. 43, No. 5 (1996), 397-399.
Note on constructing near tight wavelet frames by neural networks",
Proceedings of SPIE Conference on Wavelet Applications in
Signal and Image Processing IV,
M.A. Unser, A. Aldroubi, and A.F. Laine, ed.,
Vol. 2825 (1996), 152-162.
Limitations on the approximation capbilities of neural
networks with one hidden layer", (with C.K. Chui and H.N. Mhaskar),
Advances in Computational Mathematics, 5 (1996), 233-243.
Hankel matrices and approximation of continuous-time systems,
Approximation Theory VIII, Vol.1: Approximation and Interpolation,
C.K. Chui and L.L. Schumaker, ed., (1995), 335-342.
Hankel operators and best Hankel approximation on
the half-plane", Advances in Computational Mathematics, 2 (1994),
343-355.
Neural networks for localized approximation, (with C.K. Chui
and H.N. Mhaskar), Mathematics of Computation, Vol.
63, No. 208 (1994),
607-623.
Continuity of best Hankel approximation and convergence of
near-best approximants, (with C.K. Chui),
SIAM Journal on Control and Optimization,
Vol. 121, No. 1 (1994), 1769-1781.
Generalized wavelet decompositions of bivariate functions,
(with C.K. Chui), Proceedings of American Mathematical Society,
Vol. 121, No. 1 (1994), 125-131.
Hankel approximation and its applications, Ph.D. Dissertation,
Texas A&M University, May 1991.
On computation of minimum-norm tangent interpolation, (with
C.K. Chui and L. Zhong), Approximation Theory VI, Vol. I, C.K. Chui,
L.L. Schmaker, and J.D. Ward, ed., (1989), 137-140.
Generalized wavelet
decompositions of bivariate functions,
(with C.K. Chui), Proceedings of American Mathematical Society,
Vol. 121, No. 1 (1994), 125-131.
Realization of neural networks with one-hidden layer, (with
C.K. Chui), Multivariate Approximation: From CAGD to Wavelets,
K. Jetter and F. Utreras, ed., (1993), 77-89.
Approximation by ridge functions and neural networks with one
hidden layers, (with C.K. Chui), Journal of Approximation Theory,
Vol. 70, No. 2 (1992), 131-141.
On the convergence rate of s-numbers of compact Hankel
operators", (with C.K. Chui and J.D. Ward), Circuits Systems and Signal
Process, Vol. 11, No. 2 (1992), 353-362.
Rate of uniform convergence of rational functions corresponding
to best approximants of truncated Hankel operators, (with C.K. Chui and J.D.
Ward), Mathematics of Control, Signals, and Systems,
5 (1992), 67-79.
System reduction via truncated Hankel matrices, (with C.K. Chui
and J.D. Ward), Mathematics of Control, Signals, and Systems,
4 (1991), 161-175.
Hankel approximation and its applications, Ph.D. Dissertation,
Texas A&M University, May 1991.
On computation of minimum-norm tangent interpolation, (with
C.K. Chui and L. Zhong), Approximation Theory VI, Vol. I, C.K. Chui,
L.L. Schmaker, and J.D. Ward, ed., (1989), 137-140.
On computation of minimum-norm tangent interpolation, (with
C.K. Chui and L. Zhong), Approximation Theory VI, Vol. I, C.K. Chui,
L.L. Schmaker, and J.D. Ward, ed., (1989), 137-140.
