publications

Preprints

[14] Alexander D. Gilbert, Frances Y. Kuo, Abirami Srikumar, Density estimation for elliptic PDE with random input using preintegration and quasi-Monte Carlo methods, preprint, 2024 [arXiv]

[13] Nils Friess, Alexander D. Gilbert, Robert Scheichl, A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues, preprint, 2023. [arXiv]

Articles

[12] Tiangang Cui, Hans De Sterck, Alexander D. Gilbert, Stanislav Polishchuk and Robert Scheichl, Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems, Journal of Scientific Computing, 99, 2024. [article  or arXiv]

[11] Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan and Abirami Srikumar, Theory and construction of quasi-Monte Carlo rules for option pricing and density estimation, to appear in: A. Hinrichs, P. Kritzer, F. Pillichshammer (eds), Monte Carlo and Quasi-Monte Carlo Methods 2022, 2023. [arXiv]

[10] Alexander D. Gilbert and Robert Scheichl, Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: Efficient algorithms and numerical results,  IMA Journal of Numerical Analysis, 44, 504–535, 2024. [article or arXiv]

[9] Alexander D. Gilbert and Robert Scheichl, Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: Regularity and error analysis, IMA Journal of Numerical Analysis, 44, 466–503, 2024. [article or arXiv]

[8]  Alexander D. Gilbert, Frances Y. Kuo and Ian H. Sloan, Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities, SIAM Journal on Numerical Analysis, 61, 135–166, 2023. [article or arXiv]

[7] Alexander D. Gilbert, Frances Y. Kuo and Ian H. Sloan,  Preintegration is not smoothing when monotonicity fails, Z. Botev et al. (eds.), Advances in Modeling and Simulation, Springer, Cham, 169–191, 2022. [article  or arXiv]

[6] Alexander D. Gilbert, FrancesY. Kuo and Ian H. Sloan, Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on R^d, Mathematics of Computation, 91, 1837–1869, 2022. [article or arXiv]

[5] Alexander D. Gilbert, Ivan G. Graham, Robert Scheichl and Ian H. Sloan,  Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients, 2018 MATRIX Annals, 2020. [article or arXiv]

[4] Alexander D. Gilbert, Ivan G. Graham, Frances Y. Kuo, Robert Scheichl and Ian H. Sloan, Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients, Numerische Mathematik, 142, 863–915, 2019. [article or arXiv]

[3] Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens, and Grzegorz W. Wasilkowski, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals, SIAM Journal on Scientific Computing, 40, A3240–A3266, 2018. [article or arXiv]

[2] Alexander D. Gilbert, Frances Y. Kuo, and Ian H. Sloan, Hiding the weights—CBC blackbox algorithms with a guaranteed error bound, Mathematics and Computers in Simulation, 143, 202–214, 2018. [article or arXiv]

[1] Alexander D. Gilbert and Grzegorz W. Wasilkowski, Small superposition dimension and active set construction for multivariate integration under modest error demand, Journal of Complexity, 42, 94–109, 2017. [article or arXiv]

Theses

Alexander D. Gilbert, Algorithms for numerical integration in high and infinite dimensions: Analysis, applications and implementation, PhD Thesis, The University of New South Wales, 2018. [pdf]

Alexander D. Gilbert, Continuous-time dynamical systems: The infinitesimal generator approach and applications,  Honours Thesis, The University of New South Wales, 2013. [pdf]