By Professor Frances Kuo

Journal articles

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

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

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2011, 'Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications', Journal of Computational Physics, 230, pp. 3668 - 3694, http://dx.doi.org/10.1016/j.jcp.2011.01.023

Hickernell FJ; Kritzer P; Kuo FY; Nuyens D, 2011, 'Weighted compound integration rules with higher order convergence for all N', Numerical Algorithms, 59, pp. 161 - 183, http://dx.doi.org/10.1007/s11075-011-9482-5

Cools R; Kuo FY; Nuyens D, 2010, 'Constructing lattice rules based on weighted degree of exactness and worst case error', Computing, 87, pp. 63 - 89, http://dx.doi.org/10.1007/s00607-009-0076-1

Kuo FY; Sloan IH; Wasilkowski GW; Wozniakowski H, 2010, 'Liberating the dimension', Journal of Complexity, 26, pp. 422 - 454

Kuo FY; Sloan IH; Wasilkowski GW; Wozniakowski H, 2010, 'On decompositions of multivariate functions', Mathematics of Computation, 79, pp. 953 - 966

Kuo FY; Sloan IH; Wasilkowski GW; Waterhouse BJ, 2010, 'Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands', Journal of Complexity, 26, pp. 135 - 160, http://dx.doi.org/10.1016/j.jco.2009.07.005

Griebel M; Kuo FY; Sloan IH, 2010, 'The smoothing effect of the ANOVA decomposition', Journal of Complexity, 26, pp. 523 - 551

Kuo FY; Wasilkowski GW; Wozniakowski H, 2009, 'Lattice algorithms for multivariate L-infinity approximation in the worst-case setting', Constructive Approximation, 30, pp. 475 - 493, http://dx.doi.org/10.1007/s00365-009-9075-x

Kuo FY; Wasilkowski GW; Wozniakowski H, 2009, 'On the power of standard information for L-infinity approximation in the randomized setting', BIT Numerical Mathematics, 49, pp. 543 - 564

Kuo FY; Wasilkowski GW; Wozniakowski H, 2009, 'On the power of standard information for multivariate approximation in the worst case setting', Journal of Approximation Theory, 158, pp. 97 - 125

Joe S; Kuo FY, 2008, 'Constructing Sobol` sequences with better two-dimensional projections', SIAM journal of scientific computation, 30, pp. 2635 - 2654

Kuo FY; Sloan IH; Wozniakowski H, 2008, 'Lattice rule algorithms for multivariate approximation in the average case setting', Journal of Complexity, 24, pp. 283 - 323

Kuo FY; Wasilkowski GW; Wozniakowski H, 2008, 'Multivariate L-infinity approximation in the worst case setting over reproducing kernel Hilbert spaces', Journal of Approximation Theory, 152, pp. 135 - 160

Kuo FY; Giles M; Sloan IH; Waterhouse BJ, 2008, 'Quasi-Monte Carlo for finance applications', The ANZIAM Journal, 50, pp. C308 - C323

Kuo FY; Dunsmuir WT; Sloan IH; Wand MP; Womersley RS, 2008, 'Quasi-Monte Carlo for highly structured generalised response models', Methodology and Computing in Applied Probability, 10, pp. 239 - 275

Hesse K; Kuo FY; Sloan IH, 2007, 'A component-by-component approach to efficient numerical integration over products of spheres', Journal of Complexity, 23, pp. 25 - 51, http://dx.doi.org/10.1016/j.jco.2006.08.001

Dick J; Kritzer P; Kuo FY; Sloan IH, 2007, 'Lattice-Nystrom method for Fredholm integral equations of the second kind with convolution type kernels', Journal of Complexity, 23, pp. 752 - 772

Kuo FY; Sloan IH; Wozniakowski H, 2007, 'Periodization strategy may fail in high dimensions', Numerical Algorithms, 46, pp. 369 - 391

Cools R; Kuo FY; Nuyens D, 2006, 'Constructing embedded lattice rules for multivariate integration', SIAM journal of scientific computation, 28, pp. 2162 - 2188

Kuo FY; Wasilkowski GW; Waterhouse BJ, 2006, 'Randomly shifted lattice rules for unbounded integrands', Journal of Complexity, 22, pp. 630 - 651

Waterhouse BJ; Kuo FY; Sloan IH, 2006, 'Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions', Journal of Complexity, 22, pp. 71 - 101, http://dx.doi.org/10.1016/j.jco.2005.06.004

Dick J; Kuo FY; Pillichshammer F; Sloan IH, 2005, 'Construction algorithms for polynomial lattice rules for multivariate integration', Mathematics of Computation, 74, pp. 1895 - 1921

Kuo FY; Sloan IH, 2005, 'Lifting the curse of dimensionality', Notices of the American Mathematical Society, 52, pp. 1320 - 1328

Kuo FY; Sloan IH, 2005, 'Quasi-Monte Carlo methods can be efficient for integration over products of spheres', Journal of Complexity, 21, pp. 196 - 210

Dick J; Kuo FY, 2004, 'Reducing the construction cost of the component-by-component construction of good lattice rules', Mathematics of Computation, 73, pp. 1967 - 1988

Kuo FY; Joe S, 2003, 'Component-by-component construction of good intermediate-rank lattice rules', SIAM Journal on Numerical Analysis, 41, pp. 1465 - 1486

Kuo FY, 2003, 'Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces', Journal of Complexity, 19, pp. 301 - 320

Joe S; Kuo FY, 2003, 'Remark on algorithm 659: Implementing Sobol`s quasirandom sequence generator', ACM Transactions on Mathematical Software, 29, pp. 49 - 57

Kuo FY; Joe S, 2002, 'Component-by-component construction of good lattice rules with a composite number of points', Journal of Complexity, 18, pp. 943 - 976, http://dx.doi.org/10.1006/jcom.2002.0650

Conference Papers

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2022, 'Lattice field computations via recursive numerical integration', in Proceedings of Science

Kazashi Y; Kuo FY; Sloan IH, 2019, 'Derandomised lattice rules for high dimensional integration', in CTAC 2018 Computational Techniques and Applications Conference, Australian Mathematical Society, Newcastle, Australia, pp. C247 - C260, presented at CTAC 2018 Computational Techniques and Applications Conference, Newcastle, Australia, 27 November 2019 - 30 November 2019, http://dx.doi.org/10.21914/anziamj.v60i0.14110

Kuo FY; Nuyens D, 2016, 'Application of quasi-monte carlo methods to PDEs with random coefficients – An overview and tutorial', in Springer Proceedings in Mathematics and Statistics, Stanford, USA, pp. 53 - 71, presented at Monte Carlo and Quasi-Monte Carlo Methods 2016, Stanford, USA, 14 August 2016 - 19 August 2016, http://dx.doi.org/10.1007/978-3-319-91436-7_3

Giles MB; Kuo FY; Sloan IH, 2016, 'Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients', in Springer Proceedings in Mathematics and Statistics, Stanford, USA, pp. 265 - 281, presented at Monte Carlo and Quasi-Monte Carlo Methods 2016, Stanford, USA, 14 August 2016 - 19 August 2016, http://dx.doi.org/10.1007/978-3-319-91436-7_14

Kuo FY; Nuyens D, 2016, 'Hot new directions for Quasi-Monte Carlo research in step with applications', in Springer Proceedings in Mathematics and Statistics, Standford, USA, pp. 123 - 144, presented at Monte Carlo and Quasi-Monte Carlo Methods 2016, Standford, USA, 14 August 2016 - 19 August 2016, http://dx.doi.org/10.1007/978-3-319-91436-7_6

Dick J; Kuo FY; Peters GW; Sloan IH, 2013, 'Preface', in Springer Proceedings in Mathematics and Statistics

Dick J; Kritzer P; Kuo FY, 2006, 'Approximation of functions using digital nets', in 7th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, Ulm, Germany, presented at 7th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, Ulm, Germany, 14 August 2006 - 18 August 2006

Kuo FY; Sloan IH; Wozniakowski H, 2004, 'Lattice rules for multivariate approximation in the worst case setting', in Monte Carlo and Quasi-Monte Carlo Methods 2004, France, presented at Monte Carlo and Quasi-Monte Carlo Methods 2004, France, 07 June 2004 - 10 June 2004

Dick J; Kuo FY, 2002, 'Constructing good lattice rules with millions of points', in 5th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2002), National University of Singapore, presented at 5th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2002), National University of Singapore, 25 November 2002 - 28 November 2002

Conference Proceedings (Editor of)

Dick J; Kuo FY; Peters GW; Sloan IH; Dick J; Kuo FY; Peters GW; Sloan IH, (eds.), 2013, 'Monte Carlo and quasi-Monte Carlo methods 2012', Springer Berlin Heidelberg, Vol. 65, http://dx.doi.org/10.1007/978-3-642-41095-6

Working Papers

Cools R; Kuo FY; Nuyens D; Sloan IH, 2019, Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights, http://dx.doi.org, http://arxiv.org/abs/1910.06606v1

Cools R; Kuo FY; Nuyens D; Sloan IH, 2019, Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters, http://dx.doi.org, http://arxiv.org/abs/1910.06604v1

Kazashi Y; Kuo FY; Sloan IH, 2019, Derandomised lattice rules for high dimensional integration, http://dx.doi.org, http://arxiv.org/abs/1903.05145v1

Brown B; Griebel M; Kuo FY; Sloan IH, 2017, On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction, http://dx.doi.org, http://arxiv.org/abs/1706.00915v3

Kuo FY; Schwab C; Sloan IH, 2012, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients, http://dx.doi.org, http://arxiv.org/abs/1208.6349v2

Preprints

Gilbert AD; Kuo FY; Srikumar A, 2024, Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods, , http://dx.doi.org/10.48550/arxiv.2402.11807

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