86 citations · 242 across the 30 of their papers we have counts for
10 papers · 1 filter
High dimensional integration of kinks and jumps -- smoothing by preintegration
Andreas Griewank, Frances Y. Kuo, Hernan Leövey +1
We show how simple kinks and jumps of otherwise smooth integrands over can be dealt with by a preliminary integration with respect to a single well chosen variable.…
Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals
Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens +1
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of -variate functions. Such -variate…
Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients
Michael B. Giles, Frances Y. Kuo, Ian H. Sloan
Building on previous research which generalized multilevel Monte Carlo methods using either sparse grids or Quasi-Monte Carlo methods, this paper considers the combination of all t…
Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial
Frances Y. Kuo, Dirk Nuyens
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth…
Hot new directions for quasi-Monte Carlo research in step with applications
Frances Y. Kuo, Dirk Nuyens
This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first orde…
Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain class…
Analysis of circulant embedding methods for sampling stationary random fields
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix appearing in the circulant embedding method is always guaranteed, provided the…
Lattice rules with random achieve nearly the optimal error independently of the dimension
Peter Kritzer, Frances Y. Kuo, Dirk Nuyens +1
We analyze a new random algorithm for numerical integration of -variate functions over from a weighted Sobolev space with dominating mixed smoothness and prod…
On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction
Bruce Brown, Michael Griebel, Frances Y. Kuo +1
It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus…
Fast random field generation with -matrices
Michael Feischl, Frances Kuo, Ian H. Sloan
We use the -matrix technology to compute the approximate square root of a covariance matrix in linear cost. This allows us to generate normal and log-normal random fields on gen…