2005-2007 Activity Report for Joseph Ward

Other Relevant Items:

Research

Papers in Print

Q. T. Le Gia, F. J. Narcowich, J. D. Ward, and H. Wendland, Continuous and Discrete Least-Squares Approximation by Radial Basis Functions on Spheres, Journal of Approximation Theory , 143, (2006), 124-133.
F. J. Narcowich, P. Petrushev, and J. D. Ward, Localized Tight Frames on Spheres, SIAM Jour. of Math. Analysis , 38, (2006), 574-594.
F. J. Narcowich, P. Petrushev and J. D. Ward, Decomposition of Besov and Triebel-Lizorkin Spaces on the Sphere, J. Functional Anal., 238, (2006), 530-564.
F. J. Narcowich, J. D. Ward, and H. Wendland, Sololev Error Estimates and a Bernstein Inequality for Scattered Data Interpolation via Radial Basis Functions, Contructive Approximation , 24, (2006), 175-186.
F. J. Narcowich, X. Sun, and J. D. Ward, Approximation Power of RBFs and Their Associated SBFs: a Connection, Advances in Computational Mathematics , 27, (2007), 107-124.
F. J. Narcowich, X. Sun, J. D. Ward and H. Wendland, Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions, Foundations of Computational Mathematics , (2007), 369-390.
F. J. Narcowich, X. J. D. Ward and G. B. Wright, Divergence-free RBFs on Surfaces, Jour. of Fourier Analysis and Applic. , 13, (2007), 643-663.

Papers Accepted

J. D. Ward, Direct and Inverse Theorems for RBF-type Functions: Implications and Applications, Proceedings of Approximation Theory XII: San Antonio 2007, to appear.

Papers Submitted

E. J. Fuselier, F. J. Narcowich, J. D. Ward and G. B. Wright, Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere, submitted.

Research Conference Talks

Hour talk

``Direct and Inverse Theorems for RBF-type Functions: Implications and Applications, An Invited Plenary talk at the ``12 International Conference on Approximation Theory, March 4-8, 2007, San Antonio, Tx.
Funding source: Conference organizers.

Approximation with Interpolatory Constraints, Texas A&M at Praire View, Nov. 9, 2007
Funding source: Local expenses paid by Praire View.

``Norming Sets in Multivariate Approximation: An Overview", Constructive Function Theory, Sam Houston State Univ., Oct. 26-27, 2007.
Funding source: Local expenses paid by Sam Houston Stae Univ.

"Norming Sets in Multivariate Approximation: An Overview" An invited talk at the "Sixth International Conference on Multivariate Approximation", Dortmund, Germany, (Sept.25-Oct.1,2005).
Funding source: Conference organizers.

Half Hour talk

``Bernstein Theorems for SBFs on the n-sphere, Special session on ``Approximation on the sphere" at the ICIAM, Zurich, Switzerland, July 16-20, 2007.

"Sobolev Error Estimates for Scattered Data Interpolation on S^N ", Conference on "Interaction between Wavelets and Splines", Athens, Georgia (May 16-19, 2005).

"A Discussion of Preconditioners for Radial Basis Functions", SIAM Conference on "Geometric Design and Computing", Phoenix Arizona (Oct. 31-Nov.3, 2005).

"Sobolev Error Estimates for Scattered Data Interpolation on S^N ", (joint with F. Narcowich: presented from A&M to an audience at the) Robert Schaback birthday conference, Goettingen, Germany (11/26/05).

"A Primer on Least Squares Approxiamtion with RBFs", Sixth International Conference on "Curves and Surfaces", Avignon, Fr. (June 29-July 5, 2006).

Colloquim Talks

" Approximation Power of RBFs and Their Associated SBFs: a Connection," An hour long invited talk given on July 13, (2007) at , Germany. This was part of a 2-week stay at Gottingen (hosts: H. Wendland and R. Schaback) which was completely paid for by the host institution.

``Bernstein Theorems for SBFs on the n-sphere, An hour long invited talk given on July 12, (2004) at Technische Universitat Munchen, Germany. This was part of a 1-week stay in Munich (host: Wolfgang zu Castell). Local expenses were paid for by the host institution.

"Interpolation of Scattered Data on Spheres using SBFs: Direct and Inverse Error Estimates and a Bernstein Inequality," Dept. of Mathematics, Sam Houston State University, Oct. 12, 2006.

Funding and Fund Submissions

National Science Foundation:(joint with F.J. Narcowich) DMS--0204449. August 1, 2002 to July 31, 2005, $208,184.
National Science Foundation:(joint with F.J. Narcowich) DMS--0504353 August 1, 2005 to July 31, 2008, $204,697.
National Science Foundation:(joint with F.J. Narcowich) Proposal submitted.

Service

Extra-University Activities

Editorial board, Mathematics of Computation, 1996-Dec. 31, 2004
Editorial board, Journal of Approximation Theory, Appointment in Nov. 2004
Editorial board, Advances in Computational Mathematics, Appointment in 2000
Editorial board, Approximation Theory and Applications, 1990-present
co-edited ( with F. Narcowich) Volume 21, issues 1 & 2, of Adv. Comput. Math. (2004). This was devoted to computation and approximation on the sphere.

Departmental Activities

Departmental Service award: 2005
Committee T 2004-2006; Head of committee T in 2005
Graduate Committee 2004-2006
Wrote graduate qualifiers for 641-642 (together with R. Smith or J. Zhou), spring and fall, 2002,2003,2004

Reviewing and Refereeing

Annals of Mathematics
SIAM J. Math. Anal.
Math. Comp.
Constructive Approximation
Adv. in Comp. Math.
Proc. of AMS
Lin. Alg. and Applic.
Neural Networks
Numerous Conference Proceedings

NSF (several times) including being on the NSF panel review for optimization and computation (March 2006).

Teaching

Courses taught

Fall 2007: Math 407-501 Complex Variables.
Spring 2007: Math 304-501 Linear Algebra ; Math 304-502 Linear Algebra.
Fall 2006: Math 658 Applied Harmonic Analysis (5 students).
Spring 2006: Math 308 Differential Equations (~50 students); Math 409 Advanced Calculus I (~20 students).
Fall 2005: Math 640 Linear Algebra for Applications (17 students).
Spring 2005: Math 308-512 Differential Equations (~50 students); Math 308-513 Differential Equations (~50 students).

Graduate Students Supervised

Ph.D. student--Ed Fusilier, May 2006 (co-advisor F. J. Narcowich) Dissertation: Refined Error Estimates for Matrix-valued Radial Basis Functions.
Ph.D. student--John Paul Ward, (co-advisor F. J. Narcowich) currently advising.
Ph. D. Committee--On committee of D. Larson's student, Z. Zhang and a student of R. Eubank, Yolanda Munoz (Stat.)