Fred J. Hickernell, Ph.D.

Chair of the Department of Applied Mathematics
Professor of Applied Mathematics

312.567.8983

312.567.3135

Office:

Engineering 1 Room 208

Office Hours:

by appointment only

Education

Ph.D. - Massachusetts Institute of Technology (1981)
B.A. - Pomona College (1977)

Research & Accomplishments

Developed new measures of uniformity for designs used in laboratory and numerical experiments; established numerical error and computational complexity bounds for Monte Carlo and quasi-Monte Carlo methods

Expertise

• Computational complexity of numerical problems
• Experimental design
• Multivariate numerical approximation and integration
• Monte Carlo and quasi-Monte Carlo methods

Projects

• Fast and accurate approximation of multivariate functions
• Numerical integration of stochastic differential equations
• Uniform experimental designs
• Computational finance

Awards

• Fellow of the American Scientific Affiliation
• Fellow of the Institute of Mathematical Statistics
• Elected Member of the International Statistical Institute
• Phi Beta Kappa

Publications

G.E. Fasshauer, F.J. Hicknernell, and H. Wozniakowski, On dimension-independent rates of approximation with Gaussian kernels, SIAM J. Numer. Anal. 50 (2012) 247-271.

F.J. Hickernell, T. Muller-Gronbach, B. Niu, and K. Ritter, Deterministic multi-level algorithm on $\mathbb{R}^{mathbb{N}}$, J Complexity 27 (2011). 331-351.

F. J. Hickernell, C. Lemieux, and A. B. Owen, Control variates for quasi-Monte Carlo , Statist. Sci. 20 (2005), 1–31.

F. J. Hickernell and M. Q. Liu, Uniform designs limit aliasing, Biometrika 89 (2002), 893–904, MR2003h:62116.

F. J. Hickernell and H. Niederreiter, The existence of good extensible rank-1 lattices , J. Complexity 19 (2003), 286–300.

F. J. Hickernell and H. Wozniakowski, Integration and approximation in arbitrary dimensions, Adv.Comput. Math.12 (2000), 25–58.

F. J. Hickernell and R. X. Yue, The mean square discrepancy of scrambled (t, s)-sequences, SIAM J. Numer. Anal.(2000), 1089–1112.

F. J. Hickernell, Goodness-of-ﬁt statistics, discrepancies and robust designs, Statist. Probab. Lett. 44 (1999), 73–78.

F. J. Hickernell, A generalized discrepancy and quadrature error bound, Math. Comp. 67 (1998), 299–322.