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Preintegration is not smoothing when monotonicity fails
Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan
Preintegration is a technique for high-dimensional integration over -dimensional Euclidean space, which is designed to reduce an integral whose integrand contains kinks or jumps…
Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities
Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of indep…
Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on
Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan
We prove that a variant of the classical Sobolev space of first-order dominating mixed smoothness is equivalent (under a certain condition) to the unanchored ANOVA space on $\mathb…
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: Efficient algorithms and numerical results
Alexander D. Gilbert, Robert Scheichl
Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In…