By Dr Alexander Dominik Gilbert

Book Chapters

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 International Publishing, pp. 29 - 43, http://dx.doi.org/10.1007/978-3-030-38230-8_3

Journal articles

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

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

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; 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

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

Gilbert AD; Kuo FY; Sloan IH, 2021, Preintegration is not smoothing when monotonicity fails, , http://arxiv.org/abs/2112.11621v1

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

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; 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

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; 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

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

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