Search Results - "Kuo, Frances Y."

Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation by Kuo, Frances Y., Nuyens, Dirk

“…This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations…”
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QUASI-MONTE CARLO FINITE ELEMENT METHODS FOR A CLASS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS by KUO, FRANCES Y., SCHWAB, CHRISTOPH, SLOAN, IAN H.

“…In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial differential equations (PDEs) with random coefficients, where the…”
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Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems by KUO, FRANCES Y., SCHEICHL, ROBERT, SCHWAB, CHRISTOPH, SLOAN, IAN H., ULLMANN, ELISABETH

“…multilevel Quasi-Monte Carlo finite element discretisations and give a constructive proof of the dimension-independent convergence of the QMC rules. More…”
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Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients by Kuo, Frances Y., Schwab, Christoph, Sloan, Ian H.

“…This paper is a sequel to our previous work (Kuo et al. in SIAM J Numer Anal, 2012) where quasi-Monte Carlo (QMC) methods (specifically, randomly shifted…”
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Fast random field generation with H-matrices by Feischl, Michael, Kuo, Frances Y., Sloan, Ian H.

“…We use the H -matrix technology to compute the approximate square root of a covariance matrix in linear cost. This allows us to generate normal and log-normal…”
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HIGHER ORDER QMC PETROV–GALERKIN DISCRETIZATION FOR AFFINE PARAMETRIC OPERATOR EQUATIONS WITH RANDOM FIELD INPUTS by DICK, JOSEF, YUO, FRANCES Y., LE GIA, QUOC T., NUYENS, DIRK, SCHWAB, CHRISTOPH

“…We construct quasi–Monte Carlo methods to approximate the expected values of linear functionals of Petrov–Galerkin discretizations of parametric operator…”
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Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration by Guth, Philipp A., Kaarnioja, Vesa, Kuo, Frances Y., Schillings, Claudia, Sloan, Ian H.

“…We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation…”
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Uncertainty quantification for random domains using periodic random variables by Hakula, Harri, Harbrecht, Helmut, Kaarnioja, Vesa, Kuo, Frances Y., Sloan, Ian H.

“…We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use…”
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Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification by Kaarnioja, Vesa, Kazashi, Yoshihito, Kuo, Frances Y., Nobile, Fabio, Sloan, Ian H.

“…This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a setting…”
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Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory by Hartung, Tobias, Jansen, Karl, Kuo, Frances Y., Leövey, Hernan, Nuyens, Dirk, Sloan, Ian H.

“…•Recursive integration strategies independent of the number of integration variables are proposed.•We show lattice based cubature methods that can improve…”
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Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients by Graham, Ivan G., Kuo, Frances Y., Nuyens, Dirk, Scheichl, Rob, Sloan, Ian H.

“…In a previous paper (Graham et al. in J Comput Phys 230:3668–3694, 2011 ), the authors proposed a new practical method for computing expected values of…”
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The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth by GRIEBEL, MICHAEL, KUO, FRANCES Y., SLOAN, IAN H.

“…The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We…”
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Correction to: Fast random field generation with H-matrices by Feischl, Michael, Kuo, Frances Y., Sloan, Ian H.

“…The corrected version states the parameter range as p  ∈ 2ℕ instead of p  ∈ ℕ. The effect is to disallow non-smooth norms such as the ℓ 1 -norm for the…”
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Multivariate integration for analytic functions with Gaussian kernels by KUO, FRANCES Y., SLOAN, IAN H., WOŹNIAKOWSKI, HENRYK

“…We study multivariate integration of analytic functions defined on ℝ𝑑. These functions are assumed to belong to a reproducing kernel Hilbert space whose…”
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Periodization strategy may fail in high dimensions by Kuo, Frances Y., Sloan, Ian H., Woźniakowski, Henryk

“…We discuss periodization of smooth functions f of d variables for approximation of multivariate integrals. The benefit of periodization is that we may use…”
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Correction to: Lattice Algorithms for Multivariate L∞ Approximation in the Worst-Case Setting by Kuo, Frances Y., Wasilkowski, Grzegorz W., Woźniakowski, Henryk

“…We correct the expression for the worst-case error derived in [Kuo, Wasilkowski, Woźniakowski, Construct. Approx. 30 (2009), 475–493] and explain that the main…”
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Note on ``The smoothing effect of integration in \mathbb{R}^d and the ANOVA decomposition by Griebel, Michael, Kuo, Frances Y., Sloan, Ian H.

“…82 (2013), 383-400. We first report a mistake, in that the main result Theorem 3.1, though correct, does not as claimed apply to the Asian option pricing…”
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Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations by Dick, Josef, Kuo, Frances Y., Le Gia, Quoc T., Schwab, Christoph

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Gauss-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels by Kuo, Frances Y., Woźniakowski, Henryk

“…We study univariate integration with the Gaussian weight for a positive variance  α . This is done for the reproducing kernel Hilbert space with the Gaussian…”
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Constructing lattice rules based on weighted degree of exactness and worst case error by Cools, Ronald, Kuo, Frances Y., Nuyens, Dirk

“…Recall that an integration rule is said to have a trigonometric degree of exactness m if it integrates exactly all trigonometric polynomials of degree ≤ m . In…”
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