Research

My main research focuses on quasi-Monte Carlo methods for high dimensional integration. The goal is to design automatic, adaptive and guaranteed algorithms to compute infinite dimensional integrals.

I also collaborate with the Matlab toolbox GAIL and the top quark mass measurement as part of the CDF project at Fermilab. Both projects have free software and can be found in GAIL (Matlab Toolbox) and MCuncert (C++ package).


Articles

  • Fred J. Hickerenll, Ll. A. Jiménez Rugama, and Da Li. Adaptive quasi-Monte Carlo methods. 2016+. Manuscript in preparation.
  • L. Gilquin and Ll. A. Jiménez Rugama. Reliable error estimation for Sobol’ indices. Statistics and Computing, 2016+. Submitted for publication: hal-01358067.
  • L. Gilquin, Ll. A. Jiménez Rugama, E. Arnaud, F. J. Hickernell, H. Monod, and C. Prieur. Iterative construction of replicated designs based on Sobol’ sequences. Comptes Rendus Mathematique, 2016+. Accepted for publication: hal-01349444.
  • Ll. A. Jiménez Rugama and F. J. Hickernell, Adaptive Multidimensional Integration Based on Rank-1 Lattices. Monte Carlo and Quasi-Monte Carlo Methods 2014, pages 407–422, 2016. Springer International Publishing. ArXiv:1411.1966.
  • F. J. Hickernell and Ll. A. Jiménez Rugama, Reliable Adaptive Cubature Using Digital Sequences. Monte Carlo and Quasi-Monte Carlo Methods 2014, pages 367–383, 2016. Springer International Publishing. ArXiv:1410.8615
  • Sou-Cheng T. Choi, Fred J. Hickernell, Yuhan Ding, Lan Jiang, Lluis Antoni Jimenez Rugama, Xin Tong, Yizhi Zhang, and Xuan Zhou,GAIL: Guaranteed Automatic Integration Library (Version 2.0.0), [MATLAB Software], 2014. Available from GAIL.
  • Sou-Cheng T. Choi, Fred J. Hickernell, Yuhan Ding, Lan Jiang, Lluis Antoni Jimenez Rugama, Xin Tong, Yizhi Zhang, and Xuan Zhou,GAIL—Guaranteed Automatic Integration Library in MATLAB: Documentation for Version 2.1, [MATLAB Software], 2015. Available from GAIL. ArXiv:1503.06544