By Professor Frances Kuo

Journal articles

Brown B; Griebel M; Kuo FY; Sloan IANH, 2024, 'ON THE EXPECTED UNIFORM ERROR OF BROWNIAN MOTION APPROXIMATED BY THE LÉVY-CIESIELSKI CONSTRUCTION', Bulletin of the Australian Mathematical Society, 109, pp. 581 - 593, http://dx.doi.org/10.1017/S0004972723000850

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2024, 'Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration', Numerische Mathematik, 156, pp. 565 - 608, http://dx.doi.org/10.1007/s00211-024-01397-9

Hakula H; Harbrecht H; Kaarnioja V; Kuo FY; Sloan IH, 2024, 'Uncertainty quantification for random domains using periodic random variables', Numerische Mathematik, 156, pp. 273 - 317, http://dx.doi.org/10.1007/s00211-023-01392-6

Kuo FY; Mo W; Nuyens D, 2024, 'Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points', Constructive Approximation, http://dx.doi.org/10.1007/s00365-024-09688-y

Kuo FY; Nuyens D; Wilkes L, 2023, 'Random-prime–fixed-vector randomised lattice-based algorithm for high-dimensional integration', Journal of Complexity, 79, http://dx.doi.org/10.1016/j.jco.2023.101785

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

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2022, 'Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification', Numerische Mathematik, 150, pp. 33 - 77, http://dx.doi.org/10.1007/s00211-021-01242-3

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2021, 'Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory', Journal of Computational Physics, 443, http://dx.doi.org/10.1016/j.jcp.2021.110527

Kuo FY; Migliorati G; Nobile F; Nuyens D, 2021, 'FUNCTION INTEGRATION, RECONSTRUCTION AND APPROXIMATION USING RANK-1 LATTICES', Mathematics of Computation, 90, pp. 1861 - 1897, http://dx.doi.org/10.1090/mcom/3595

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2021, 'A quasi-monte carlo method for optimal control under uncertainty', SIAM-ASA Journal on Uncertainty Quantification, 9, pp. 354 - 383, http://dx.doi.org/10.1137/19M1294952

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://arxiv.org/abs/2103.16075v3

Ganesh M; Kuo FY; Sloan IH, 2021, 'Quasi-monte carlo finite element analysis for wave propagation in heterogeneous random media', SIAM-ASA Journal on Uncertainty Quantification, 9, pp. 106 - 134, http://dx.doi.org/10.1137/20M1334164

Cools R; Kuo FY; Nuyens D; Sloan IH, 2020, 'Fast Component-by-Component Construction of Lattice Algorithms for Multivariate Approximation with Pod and Spod Weights', Mathematics of Computation, 90, pp. 787 - 812, http://dx.doi.org/10.1090/MCOM/3586

Bilyk D; Hinrichs A; Kuo FY; Ritter K, 2020, 'Guest editors’ preface', Journal of Complexity, 61, http://dx.doi.org/10.1016/j.jco.2020.101511

Kuo FY; Wasilkowski GW; Woźniakowski H, 2020, 'Correction to: Lattice Algorithms for Multivariate L∞ Approximation in the Worst-Case Setting (Constructive Approximation, (2009), 30, 3, (475-493), 10.1007/s00365-009-9075-x)', Constructive Approximation, 52, pp. 177 - 179, http://dx.doi.org/10.1007/s00365-020-09498-y

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2020, 'Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification', Numerische Mathematik, 150, pp. 33 - 77, http://dx.doi.org/10.1007/s00211-021-01242-3

Kaarnioja V; Kuo FY; Sloan IH, 2020, 'Uncertainty quantification using periodic random variables', SIAM Journal on Numerical Analysis, 58, pp. 1068 - 1091, http://dx.doi.org/10.1137/19M1262796

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

Feischl M; Kuo FY; Sloan IH, 2019, 'Correction to: Fast random field generation with H-matrices (Math. (2018) 140:639–676, (10.1007/s00211-018-0974-2))', Numerische Mathematik, 142, pp. 787, http://dx.doi.org/10.1007/s00211-019-01033-x

Kritzer P; Kuo FY; Nuyens D; Ullrich M, 2019, 'Lattice rules with random n achieve nearly the optimal O(n ^{−α−1∕2} ) error independently of the dimension', Journal of Approximation Theory, 240, pp. 96 - 113, http://dx.doi.org/10.1016/j.jat.2018.09.011

Griewank A; Kuo FY; Leövey H; Sloan IH, 2018, 'High dimensional integration of kinks and jumps—Smoothing by preintegration', Journal of Computational and Applied Mathematics, 344, pp. 259 - 274, http://dx.doi.org/10.1016/j.cam.2018.04.009

Feischl M; Kuo FY; Sloan IH, 2018, 'Fast random field generation with H-matrices', Numerische Mathematik, 140, pp. 639 - 676, http://dx.doi.org/10.1007/s00211-018-0974-2

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2018, 'Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients', Numerische Mathematik, 140, pp. 479 - 511, http://dx.doi.org/10.1007/s00211-018-0968-0

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2018, 'Analysis of circulant embedding methods for sampling stationary random fields', SIAM Journal on Numerical Analysis, 56, pp. 1871 - 1895, http://dx.doi.org/10.1137/17M1149730

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

Kuo FY; Nuyens D; Plaskota L; Sloan IH; Wasilkowski GW, 2017, 'Infinite-dimensional integration and the multivariate decomposition method', Journal of Computational and Applied Mathematics, 326, pp. 217 - 234, http://dx.doi.org/10.1016/j.cam.2017.05.031

Kuo FY; Scheichl R; Schwab C; Sloan IH; Ullmann E, 2017, 'Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems', Mathematics of Computation, 86, pp. 2827 - 2860, http://dx.doi.org/10.1090/mcom/3207

Kuo FY; Sloan IH; Woźniakowski H, 2017, 'Multivariate integration for analytic functions with Gaussian Kernels', Mathematics of Computation, 86, pp. 829 - 853, http://dx.doi.org/10.1090/mcom/3144

Griebel M; Kuo FY; Sloan IH, 2017, 'Note on "The smoothing effect of integration in R^d and the ANOVA decomposition"', Mathematics of Computation, 86, pp. 1847 - 1854, http://dx.doi.org/10.1090/mcom/3172

Griebel M; Kuo FY; Sloan IH, 2017, 'The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth', Mathematics of Computation, 86, pp. 1855 - 1876, http://dx.doi.org/10.1090/mcom/3171

Kuo FY; Nuyens D, 2016, 'Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation', Foundations of Computational Mathematics, 16, pp. 1631 - 1696, http://dx.doi.org/10.1007/s10208-016-9329-5

Cools R; Kuo FY; Nuyens D; Suryanarayana G, 2016, 'Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions', Journal of Complexity, 36, pp. 166 - 181, http://dx.doi.org/10.1016/j.jco.2016.05.004

Dick J; Kuo FY; Le Gia QT; Schwab C, 2016, 'Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations', SIAM Journal on Numerical Analysis, 54, pp. 2541 - 2568, http://dx.doi.org/10.1137/16M1078690

Kuo FY; Plaskota L; Wasilkowski GW, 2016, 'Optimal algorithms for doubly weighted approximation of univariate functions', Journal of Approximation Theory, 201, pp. 30 - 47, http://dx.doi.org/10.1016/j.jat.2015.08.007

Graham IG; Kuo FY; Nichols JA; Scheichl R; Schwab C; Sloan IH, 2015, 'Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients', Numerische Mathematik, 131, pp. 329 - 368, http://dx.doi.org/10.1007/s00211-014-0689-y

Gnewuch M; Kuo FY; Niederreiter H; Woźniakowski H, 2015, 'Guest editors' preface', Journal of Complexity, 31, pp. vi, http://dx.doi.org/10.1016/S0885-064X(15)00032-1

Kuo FY; Schwab C; Sloan IH, 2015, 'Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients', Foundations of Computational Mathematics, 15, pp. 411 - 449, http://dx.doi.org/10.1007/s10208-014-9237-5

Dick J; Kuo FY; Gia QTL; Schwab C; Le Gia Q, 2015, 'Fast QMC matrix-vector multiplication', SIAM Journal on Scientific Computing, 37, pp. A1436 - A1450, http://dx.doi.org/10.1137/151005518

Gnewuch M; Kuo FY; Niederreiter H; Woźniakowski H, 2014, 'Uniform Distribution Theory and Applications', Oberwolfach Reports, 10, pp. 2837 - 2917, http://dx.doi.org/10.4171/owr/2013/49

Nichols JA; Kuo FY, 2014, 'Fast CBC construction of randomly shifted lattice rules achieving O (n ^{-1 + δ}) convergence for unbounded integrands over ℝ^s in weighted spaces with POD weights', Journal of Complexity, 30, pp. 444 - 468, http://dx.doi.org/10.1016/j.jco.2014.02.004

Dick J; Kuo FY; Le Gia QT; Nuyens D; Schwab C, 2014, 'Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs', SIAM Journal on Numerical Analysis, 52, pp. 2676 - 2702, http://dx.doi.org/10.1137/130943984

Sinescu V; Kuo FY; Sloan IH, 2013, 'On the Choice of Weights in a Function Space for Quasi-Monte Carlo Methods for a Class of Generalised Response Models in Statistics', Springer Proceedings in Mathematics and Statistics, 65, pp. 631 - 647, http://dx.doi.org/10.1007/978-3-642-41095-6_33

Kuo FY; Sloan IH; Schwab C, 2013, 'Erratum: Quasi-Monte Carlo methods for high-dimensional integration: The standard (weighted hilbert space) setting and beyond (ANZIAM Journal (2011) 53 (1-37))', ANZIAM Journal, 54, pp. 216 - 219, http://dx.doi.org/10.1017/S144618111300014X

Dick J; Kuo FY; Sloan IH, 2013, 'High dimensional numerical integration - the Quasi-Monte Carlo way', Acta Numerica, 22, pp. 133 - 288, http://dx.doi.org/10.1017/S0962492913000044

Griebel M; Kuo FY; Sloan IH, 2013, 'The smoothing effect of integration in $R^d$ and the ANOVA decomposition', Mathematics of Computation, 82, pp. 383 - 400

Kuo FY; Schwab C; Sloan IH, 2012, 'Erratum: Quasi-monte carlo methods for high-dimensional integration: The standard (weighted hilbert space) setting and beyond (ANZIAM Journal (2011) 53 (1-37) DOI: 10.1017/S1446181112000077)', ANZIAM Journal, 53, pp. 251, http://dx.doi.org/10.1017/S1446181112000144

Kuo FY; Wozniakowski H, 2012, 'Gauss-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels', BIT Numerical Mathematics, 52, pp. 425 - 436, http://dx.doi.org/10.1007/s10543-011-0358-9

Kuo FY; Schwab CH; Sloan IH, 2012, 'Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients', SIAM Journal on Numerical Analysis, 50, pp. 3351 - 3374, http://dx.doi.org/10.1137/110845537

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