By Dr Alexander Dominik Gilbert

Book Chapters

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

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

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, http://dx.doi.org/10.1007/978-3-030-38230-8_3

Journal articles

Bartel F; Gilbert A; Kuo F; Sloan I, 2026, 'Minimal subsampled rank-1 lattices for multivariate approximation with optimal convergence rate', Mathematics of Computation, http://dx.doi.org/10.1090/mcom/4212

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

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

Cui T; De Sterck H; Gilbert AD; Polishchuk S; Scheichl R, 2024, 'Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems', Journal of Scientific Computing, 99, http://dx.doi.org/10.1007/s10915-024-02539-9

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

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

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

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

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

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

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

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

Gilbert AD; Giles MB; Kuo FY; Sloan IH; Srikumar A, 2026, Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients, http://dx.doi.org/10.48550/arxiv.2504.15810

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, http://dx.doi.org/10.48550/arxiv.2509.25753

Bartel F; Gilbert AD; Kuo FY; Sloan IH, 2026, Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate, http://dx.doi.org/10.48550/arxiv.2506.07729

Friess N; Gilbert AD; Scheichl R, 2024, A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues, http://dx.doi.org/10.48550/arxiv.2312.02847

Gilbert AD; Kuo FY; Srikumar A, 2024, Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods, http://dx.doi.org/10.48550/arxiv.2402.11807

Cui T; De Sterck H; Gilbert AD; Polishchuk S; Scheichl R, 2024, Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems, http://dx.doi.org/10.48550/arxiv.2303.03673

Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2023, Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation, http://dx.doi.org/10.48550/arxiv.2212.11493

Gilbert AD; Kuo FY; Sloan IH, 2022, Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities, http://dx.doi.org/10.48550/arxiv.2112.10308

Gilbert AD; Kuo FY; Sloan IH, 2021, Preintegration is not smoothing when monotonicity fails, http://dx.doi.org/10.48550/arxiv.2112.11621

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

Gilbert AD; Graham IG; Kuo FY; Scheichl R; Sloan IH, 2019, Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients, http://dx.doi.org/10.48550/arxiv.1808.02639

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

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

Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2018, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals, http://dx.doi.org/10.48550/arxiv.1712.06782

Back to profile page