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Dr Alexander Gilbert

Dr Alexander Gilbert

Lecturer

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 | 2024
    Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2024, 'Theory and Construction of Quasi-Monte Carlo Rules for Asian Option Pricing and Density Estimation', in , pp. 277 - 295, http://dx.doi.org/10.1007/978-3-031-59762-6_13
    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, 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 MATRIX Book Series, Springer International Publishing, pp. 29 - 43, http://dx.doi.org/10.1007/978-3-030-38230-8_3
  • Journal articles | 2025
    Friess N; Gilbert AD; Scheichl R, 2025, 'A Complex-Projected Rayleigh Quotient Iteration for Targeting Interior Eigenvalues', SIAM Journal on Matrix Analysis and Applications, 46, pp. 626 - 647, http://dx.doi.org/10.1137/23m1622155
    Journal articles | 2025
    Gilbert AD; Kuo FY; Srikumar A, 2025, 'DENSITY ESTIMATION FOR ELLIPTIC PDE WITH RANDOM INPUT BY PREINTEGRATION AND QUASI-MONTE CARLO METHODS', SIAM Journal on Numerical Analysis, 63, pp. 1025 - 1054, http://dx.doi.org/10.1137/24M1640070
    Journal articles | 2024
    Cui T; De Sterck H; Gilbert AD; Polishchuk S; Scheichl R, 2024, 'Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems.', J Sci Comput, 99, pp. 77, http://dx.doi.org/10.1007/s10915-024-02539-9
    Journal articles | 2024
    Gilbert AD; Scheichl R, 2024, 'Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: regularity and error analysis', IMA Journal of Numerical Analysis, 44, pp. 466 - 503, http://dx.doi.org/10.1093/imanum/drad011
    Journal articles | 2024
    Gilbert AD; Scheichl R, 2024, 'Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: efficient algorithms and numerical results', IMA Journal of Numerical Analysis, 44, pp. 504 - 535, http://dx.doi.org/10.1093/imanum/drad009
    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 | 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 | 2025
    Bartel F; Gilbert AD; Kuo FY; Sloan IH, 2025, Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate, http://dx.doi.org/10.48550/arxiv.2506.07729
    Preprints | 2025
    Gilbert AD; Giles MB; Kuo FY; Sloan IH; Srikumar A, 2025, Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients, http://arxiv.org/abs/2504.15810v1
    Preprints | 2025
    Gilbert AD; Kuo FY; Nuyens D; Pash G; Sloan IH; Willcox KE, 2025, Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation, http://dx.doi.org/10.48550/arxiv.2509.25753
    Preprints | 2024
    Gilbert AD; Kuo FY; Srikumar A, 2024, Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods, http://arxiv.org/abs/2402.11807v2
    Preprints | 2023
    Cui T; De Sterck H; Gilbert AD; Polishchuk S; Scheichl R, 2023, Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems, http://dx.doi.org/10.48550/arxiv.2303.03673
    Preprints | 2023
    Friess N; Gilbert AD; Scheichl R, 2023, A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues, http://dx.doi.org/10.48550/arxiv.2312.02847
    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://arxiv.org/abs/2212.11493v2
    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://arxiv.org/abs/2103.16075v3
    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://arxiv.org/abs/1901.10470v1
    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://arxiv.org/abs/1808.02639v3
    Preprints | 2018
    Gilbert AD; Kuo FY; Sloan IH, 2018, Hiding the weights -- CBC black box algorithms with a guaranteed error bound, http://arxiv.org/abs/1810.03394v1
    Preprints | 2017
    Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2017, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals, http://arxiv.org/abs/1712.06782v3

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.