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Dr Alexander Gilbert

Dr Alexander Gilbert

Lecturer

PhD in Applied Mathematics, 91色情片 Sydney, 2018

BSc (Hons) in Applied Mathematics, 91色情片 Sydney, 2013

Science
School of Mathematics & Statistics

Alexander Gilbert completed a BSc (Hons) in Applied Mathematics at 91色情片 Sydney in 2013, followed by a PhD in Applied Mathematics in 2018 also at 91色情片. 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 91色情片 to work as a Postdoctoral Research Fellow.
  • Book Chapters | 2024
    Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2024, 'Theory and聽Construction of聽Quasi-Monte Carlo Rules for聽Asian Option Pricing and聽Density Estimation', in , pp. 277 - 295,
    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,
    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 Nature, pp. 29 - 43,
  • Journal articles | 2026
    Bartel F; Gilbert A; Kuo F; Sloan I, 2026, 'Minimal subsampled rank-1 lattices for multivariate approximation with optimal convergence rate', Mathematics of Computation,
    Journal articles | 2026
    Gilbert AD; Giles MB; Kuo FY; Sloan IH; Srikumar A, 2026, 'Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients', Numerische Mathematik,
    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,
    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,
    Journal articles | 2024
    Cui T; De Sterck H; Gilbert AD; Polishchuk S; Scheichl R, 2024, 'Multilevel Monte Carlo Methods for Stochastic Convection鈥揇iffusion Eigenvalue Problems', Journal of Scientific Computing, 99,
    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,
    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,
    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,
    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,
    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,
    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,
    Journal articles | 2018
    Gilbert AD; Kuo FY; Sloan IH, 2018, 'Hiding the weights鈥擟BC black box algorithms with a guaranteed error bound', Mathematics and Computers in Simulation, 143, pp. 202 - 214,
    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,
  • Preprints | 2026
    Bartel F; Gilbert AD; Griebel M; Kuo FY; Sloan IH, 2026, A higher order lattice-based method for high-dimensional numerical integration using periodization
    Preprints | 2026
    Bartel F; Gilbert AD; Kuo FY; Sloan IH, 2026, Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate,
    Preprints | 2026
    Gilbert AD; Giles MB; Kuo FY; Sloan IH; Srikumar A, 2026, Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients,
    Preprints | 2026
    Gilbert AD; Kuo FY; Nuyens D; Pash G; Sloan IH; Willcox KE, 2026, Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation,
    Preprints | 2024
    Cui T; De Sterck H; Gilbert AD; Polishchuk S; Scheichl R, 2024, Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems,
    Preprints | 2024
    Friess N; Gilbert AD; Scheichl R, 2024, A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues,
    Preprints | 2024
    Gilbert AD; Kuo FY; Srikumar A, 2024, Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods,
    Preprints | 2023
    Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2023, Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation,
    Preprints | 2022
    Gilbert AD; Kuo FY; Sloan IH, 2022, Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities,
    Preprints | 2021
    Gilbert AD; Kuo FY; Sloan IH, 2021, Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$,
    Preprints | 2021
    Gilbert AD; Kuo FY; Sloan IH, 2021, Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$,
    Preprints | 2021
    Gilbert AD; Kuo FY; Sloan IH, 2021, Preintegration is not smoothing when monotonicity fails,
    Preprints | 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,
    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,
    Preprints | 2018
    Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2018, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals,
    Preprints | 2018
    Gilbert AD; Kuo FY; Sloan IH, 2018, Hiding the weights -- CBC black box algorithms with a guaranteed error bound,
    Preprints | 2017
    Gilbert AD; Wasilkowski GW, 2017, Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand,

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.