Fred J. Hickernell

  • Professor of Applied Mathematics

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Education

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

Research Interests

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

Professional Affiliations & Memberships

Awards

  • Fellow of the Society for Industrial and Applied Mathematics
  • Fellow of the American Scientific Affiliation
  • Fellow of the Institute of Mathematical Statistics
  • Elected Member of the International Statistical Institute
  • Phi Beta Kappa

Publications

S.-C.T. Choi, Y. Ding, F.J. Hickernell, R. Jagadeeswaran, L. Jiang, Ll.A. Jiménez Rugama, D. Li, X. Tong, K. Zhang, Y. Zhang, and X. Zhou, GAIL: Guaranteed Automatic Integration Library (versions 1.0–2.3), MATLAB software, 2013–2019.

F.J. Hickernell and Ll. A. Jiménez Rugama, Reliable adaptive cubature using digital sequences}, Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014 (R. Cools and D. Nuyens, eds.), Springer Proceedings in Mathematics and Statistics, vol. 163, Springer-Verlag, Berlin, 2016, pp. 367–383.

N. Clancy, Y. Ding, C. Hamilton, F.J. Hickernell, and Y. Zhang, The cost of deterministic, adaptive, automatic algorithms: Cones, not balls, J. Complexity, 30, (2014), 21–45, DOI 10.1016/j.jco.2013.09.002.

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

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

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

Projects

  • Fast and accurate approximation of multivariate functions
  • Numerical integration of stochastic differential equations
  • Uniform experimental designs
  • Automatic algorithms for integration and approximation

Expertise

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