Fred J. Hickernell , Ph.D.
ProfessorChair
Applied Mathematics
Office: Engineering 1 Room 208
10 W. 32nd
Chicago, IL 60616
Office Hours: by appointment only
Phone: 312.567.8983
Fax: 312.567.3135
Email: hickernell_AT_iit_DOT_edu
Web: click here
Expertise
- Computational complexity of numerical problems
- Experimental design
- Multivariate numerical approximation and integration
- Monte Carlo and quasi-Monte Carlo methods
Education
- Ph.D. - Massachusetts Institute of Technology (1981)
- B.A .- Pomona College (1977)
Curriculum Vitae
Research & Major 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
Current Projects
- Fast and accurate approximation of multivariate functions
- Numerical integration of stochastic differential equations
- Uniform experimental designs
- Computational finance
Awards/Honors
- Fellow of the American Scientific Affiliation
- Fellow of the Institute of Mathematical Statistics
- Elected Member of the International Statistical Institute
- Phi Beta Kappa
Patents
Books
Selected Publications
G.E. Fasshaurer, F.J. Hicknernell, amd 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.
Professional Society Memberships
- American Mathematical Society
- American Scientific Affiliation
- American Statistical Association
- Hong Kong Statistical Society
- Institute for Operations Research and The Management
- Institute of Electrical and Electronics Engineers (Senior Member)
- Institute of Mathematical Statistics
- International Statistical Institute
- Mathematical Association of America
- Sigma Xi
- Society for Industry and Applied Mathematics (SIAM)
