Research Interests:
My primary objective is to develop new theories (and their corresponding
algorithms) for data approximation:
Given a set of data (possibly contaminated), construct
a function/surface which is close in some sense to the original
(unknown) function/image/surface. Specifically, my research interests are
as follows: Subdivision Scheme, Wavelet, Scattered Data Approximation
by RBF (Radial Basis functions), Image Processing and Numerical PDE.
Papers:

(with N. Dyn, D. Levin),
Some Tools for Analyzing NonUniform Subdivision Schemes,
Constructive Approximation, to appear, 2014.

(with Y. Lee, C. Micchelli),
On convergence of flat multivariate interpolation
by translation kernels with finite smoothness
Constructive Approximation,
accepted, 2014.

(with S. Lee, Y. Lee),
A Framework for Moving Least Squares Method with Total Variation
Minimizing Regularization,
Journal of Mathematical Imaging and Vision , 48, 566582, 2014.

(with S. Jang, et al),
Dataadapted moving least squares method for 3D image interpolaiton.
Minimizing Regularization, Phys. in Med. and Biol.,
58, 84018418, 2013.

(with Y. Ha, Y. Lee),
Modified Essentially NonOscillatory schemes based on
exponential polynomial interpolation for hyperbolic conservation law,
SIAM J. Numer. Anal.
accepted, 2013

B. Jung, Y. Lee and J. Yoon,
A family of subdivisionscheme reproducing exponential polynomial,
J. of Math. Anal. and Appl. , 402 (1), 207219, 2013

(with B. Jung, H. Kim, Y. Ju Lee),
Exponential polynomial reproduction property of nonstationary
subdivision schemes and normalized exponential Bsplines,
Advances in Comp. Math., 38 (3), 647666, 2013

(with Y. Ha, C. Kim, Y. Lee),
An improved weighted essentially nonoscillatory scheme
with a new smoothness indicator, J. of Comp. Physics ,
232, 6886, 2013.

Youngsoo Ha, Changho Kim, Yeon Ju Lee and Jungho Yoon,
Mapped WENO schemes based on a new smoothness indicator
for HamiltonJacobi Equations, J. of Math. Anal. and Appl. ,
vol. 394, 670682, 2012.

(with K. Kwon D. Lee)
BandLimited Scaling Functions with Oversampling Property,
IEICE Trans. Fund. of Ele. Comm. and Comp. E95A, 661665, (2012)

(with Y. Lee, M. Lee),
Sobolevtype LpApproximation Orders of
Radial Basis Function Interpolation to Functions in Fractional
Sobolev Spaces,
IMA Journal of Numerical Analysis, 32, 279293, 2012.

(with Y. Lee),
Analysis of Compactly Supported Nonstationary biorthogonal
Wavelwet Systems based on Exponential Bsplines,
Abstract Applied Analysis, vol 2011, 10853375, 2011.

(with S. Hasik, M. Lee, Y. Lee),
Some issues on interpolation matrices of locally scaled
radial basis functions,
Applied Mathematics and Computation,
217, 50115014 (2011).

(with Y. Lee),
Nonliear Image Zooming Upsampling Method based on Radial
Basis Function Interplation,
IEEE Transactions on Image Processing ,
Vol 19 Issue 10, 2682  2692 (2010)

(with H. Kim, R. Kim, Y. Lee),
QuasiInterpolatory Refinable Functions and Construction of
Biorthogonal Wavelet Systems,
Adv. in Comp. Math , 33, no. 3, 255283, (2010).

(with Y. Lee),
Nonstationary Subdivision Schemes for Surface Interpolation
based on Exponential Polynomials,
Applied Numerical Mathematics ,
vol. 60, 130141 (2010).

(with Y. Lee),
Analysis of Stationary Subdivision Schemes for Curve Designs based on
Radial Basis Function Interpolation,
Applied Mathematics and Computation,
vol. 215, 38513859 (2010).

(with R. Archibald, A. Gelb),
Determining the Locations and Discontinuities in the Derivatives
of Functions,
Applied Numerical Mathematics , Vol 58, 577592 (2008).

Yeon Ju Lee, Gang Jun Yoon, Jungho Yoon,
Convergence Property of Increasingly Flat Radial Basis function
Interpolation to Polynomial Interpolation,
PostScriptfile,
SIAM J. Mathematical Analysis, Vol 39 537553, (2007).

Nira Dyn, David Levin, and Jungho Yoon,
Analysis of Univariate Nonstationary Subdivision Schemes
with Application to GaussianBased Interpolatory Schemes,
SIAM J. Mathematical Analysis, Vol 39, 470488 (2007).

Changho Kim, Sang Dong Kim, Jungho Yoon,
A collocation leastsquares approximation for
secondorder elliptic partial differential equations
Applied . Comp. Math. , to appear, (2007).

Choi, Y.J. Lee, J. Yoon, B.G. Lee, Y.J. Kim,
A New Class of Nonstationary Interpolatory Subdivision Schemes based on
Exponential Polynomials,
SpringerLink, Geometric Modeling and Processing  GMP 2006:
PDFfile
Lecture Notes in Computer Science Vol 4077, pp.563570, 2006.

Byung Gook Lee, Yeon Ju Lee, Jungho Yoon,
Stationary Binary Subdivision Schemes Using
Radial Basis Function Interpolation,
PDFfile
Advances in Comp. Math. Vol 25. 5772 (2006).

Sung Woo Choi, Byung Gook Lee, Yeon Ju Lee, Jungho Yoon,
Stationary Subdivision Schemes Reproducing Polynomials,
PDFfile
Computer Aided Geometric Design , Vol 23, 351360 (2006).

Changho Kim, Sangdong Kim, Yong Hun Lee, Jungho Yoon,
Convergence analysis for a secondorder elliptic
Equation by a collocation method using scattered points,
PDFfile
Journal of Comp. Appl. Math. ,
Vol 186 (2006) no. 1, 450465,

Rick Archibald, Anne Gelb, Jungho Yoon,
Polynomial Fitting for Edge Detection in irregularly Sampled
Signals and Images,
PDFfile
SIAM Numer. Analysis , Vol. 43, 259279, (2005).

Jungho Yoon,
Improved Accuracy of $L_p$Approximation to Derivatives
by Radial Basis Function Interpolation
Appl. Math. Comp. 161 (2005), no. 1, 109119.

Jungho Yoon,
On the stationary $L\sb p$approximation power to derivatives by radial basis
function interpolation. Appl. Math. Comp. 150 (2004), no. 3, 875887.

Jungho Yoon,
$L_p$ Error Estimates for `Shifted' Surface Spline Interpolation
on Sobolev Space,
Mathematics of Computation, 72 (2003), 243, 13491367.
PostScriptfile,
PDFfile

Jungho Yoon,
A Nonstationary Approximation Scheme on Scattered Centers in $R^d$
by Radial Basis functions,
Special Issue on "Wavelets and Approximation Theory",
Journal of Comp. Appl. Math. ,
Vol 155 (2003) no. 1, 163175,
PostScriptfile,
PDFfile

Jungho Yoon,
Spectral Approximation Orders of Radial
Basis Function Interpolation on the Sobolev Space,
SIAM J. Math Anal., Vol. 33, No 4, 946958, (2001).
PostScriptfile,
PDFfile
 Jungho Yoon,
Approximation in $L_p(R^d)$ from a space spanned by the
scattered shifts of a radial basis function,
Constructive Approximation 17 (2001), no. 2, 227247.
PostScriptfile,
PDFfile
 Jungho Yoon,
Computational Aspects of Approximation to Scattered Data by Using
`Shifted'
ThinPlate Spline, Advances in Comp. Math. 14 (2001), no. 4, 329359.
PostScriptfile,
PDFfile
 Jungho Yoon,
Interpolation by Radial Basis Functions on Sobolev Space,
Journal of Approx. Theory 112 (2001), no. 1, 115.
PostScriptfile,
PDFfile

Jungho Yoon,
Approximation by Conditionally Positive Definite Functions
With Finitely Many Centers,
Trends in Approximation Theory, K. Kopotun, T. Lyche, and
M. Neamtu (eds.), Vanderbilt University Press,
Nashville, (2001), 437446.
PostScriptfile ,
PDFfile

Jungho Yoon,
Approximation to Scattered Data,
PostScriptfile,
PDFfile, Ph.D. Thesis, 1998,
University of WisconsinMadison, USA.