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Dr Alexander Gilbert

Dr Alexander Gilbert

Research Associate

PhD in Applied Mathematics, UNSW Sydney, 2018

BSc (Hons) in Applied Mathematics, UNSW Sydney, 2013

Science
School of Mathematics & Statistics

Alexander Gilbert completed a BSc (Hons) in Applied Mathematics at UNSW Sydney in 2013, followed by a PhD in Applied Mathematics in 2018 also at UNSW. For both degrees his focus was on computational mathematics. After completing his PhD, Dr Gilbert spent two years as a Postdoctoral Research Fellow in Germany at the University of Heidelberg from 2018-2020. In late 2020, he returned to UNSW to work as a Postdoctoral Research Fellow.
  • Book Chapters | 2022
    Gilbert AD; Kuo FY; Sloan IH, 2022, 'Preintegration is Not Smoothing When Monotonicity Fails', in Advances in Modeling and Simulation: Festschrift for Pierre L'Ecuyer, Springer International Publishing, pp. 169 - 191, http://dx.doi.org/10.1007/978-3-031-10193-9_9
    Book Chapters | 2020
    Gilbert AD; Graham IG; Scheichl R; Sloan IH, 2020, 'Bounding the Spectral Gap for an Elliptic Eigenvalue Problem with Uniformly Bounded Stochastic Coefficients', in 2018 MATRIX Annals, Springer International Publishing, pp. 29 - 43, http://dx.doi.org/10.1007/978-3-030-38230-8_3
  • Journal articles | 2023
    Gilbert AD; Kuo FY; Sloan IH, 2023, 'ANALYSIS OF PREINTEGRATION FOLLOWED BY QUASI-MONTE CARLO INTEGRATION FOR DISTRIBUTION FUNCTIONS AND DENSITIES', SIAM Journal on Numerical Analysis, 61, pp. 135 - 166, http://dx.doi.org/10.1137/21M146658X
    Journal articles | 2023
    Gilbert AD; Scheichl R, 2023, 'Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: regularity and error analysis', IMA Journal of Numerical Analysis, http://dx.doi.org/10.1093/imanum/drad011
    Journal articles | 2023
    Gilbert AD; Scheichl R, 2023, 'Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: efficient algorithms and numerical results', IMA Journal of Numerical Analysis, http://dx.doi.org/10.1093/imanum/drad009
    Journal articles | 2022
    Gilbert AD; Kuo FY; Sloan IH, 2022, 'EQUIVALENCE BETWEEN SOBOLEV SPACES OF FIRST-ORDER DOMINATING MIXED SMOOTHNESS AND UNANCHORED ANOVA SPACES ON Rd', Mathematics of Computation, 91, pp. 1837 - 1869, http://dx.doi.org/10.1090/MCOM/3718
    Journal articles | 2019
    Gilbert AD; Graham IG; Kuo FY; Scheichl R; Sloan IH, 2019, 'Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients', Numerische Mathematik, 142, pp. 863 - 915, http://dx.doi.org/10.1007/s00211-019-01046-6
    Journal articles | 2018
    Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2018, 'Efficient implementations of the multivariate decomposition method for approximating infinite-variate integrals', SIAM Journal on Scientific Computing, 40, pp. A3240 - A3266, http://dx.doi.org/10.1137/17M1161890
    Journal articles | 2018
    Gilbert AD; Kuo FY; Sloan IH, 2018, 'Hiding the weights—CBC black box algorithms with a guaranteed error bound', Mathematics and Computers in Simulation, 143, pp. 202 - 214, http://dx.doi.org/10.1016/j.matcom.2016.06.005
    Journal articles | 2017
    Gilbert AD; Wasilkowski GW, 2017, 'Small superposition dimension and active set construction for multivariate integration under modest error demand', Journal of Complexity, 42, pp. 94 - 109, http://dx.doi.org/10.1016/j.jco.2017.03.001
  • Preprints | 2022
    Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2022, Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation, , http://dx.doi.org/10.48550/arxiv.2212.11493
    Preprints | 2021
    Gilbert AD; Kuo FY; Sloan IH, 2021, Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities, , http://arxiv.org/abs/2112.10308v5
    Preprints | 2021
    Gilbert AD; Kuo FY; Sloan IH, 2021, Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$, , http://dx.doi.org/10.48550/arxiv.2103.16075
    Preprints | 2021
    Gilbert AD; Kuo FY; Sloan IH, 2021, Preintegration is not smoothing when monotonicity fails, , http://arxiv.org/abs/2112.11621v1
    Preprints | 2019
    Gilbert AD; Graham IG; Scheichl R; Sloan IH, 2019, Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients, , http://dx.doi.org/10.48550/arxiv.1901.10470
    Preprints | 2018
    Gilbert AD; Graham IG; Kuo FY; Scheichl R; Sloan IH, 2018, Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients, , http://dx.doi.org/10.48550/arxiv.1808.02639
    Preprints | 2018
    Gilbert AD; Kuo FY; Sloan IH, 2018, Hiding the weights -- CBC black box algorithms with a guaranteed error bound, , http://dx.doi.org/10.48550/arxiv.1810.03394
    Preprints | 2017
    Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2017, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals, , http://dx.doi.org/10.48550/arxiv.1712.06782

Dr Gilbert's research is on computational mathematics and numerical analysis. He is interested in numerical methods for approximating integrals with very high dimension, with a particular focus on applications coming from uncertainty quantification. His research spans a broad range of areas of numerical integration, including algorithms, software implementation, new applications in uncertainty quantification, numerical analysis/theory and quasi-Monte Carlo quadrature rules.