Fast Component-By-Component Construction of Rank-1 Lattice Rules for (Non-)Primes (Part II). - Dirk Nuyens; Ronald Cools (Algorithms and Complexity for Continuous Problems, 2004)

Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points. - Dirk Nuyens; Ronald Cools (J. Complex., 2006)

Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces. - Dirk Nuyens; Ronald Cools (Math. Comput., 2006)

Constructing Embedded Lattice Rules for Multivariate Integration. - Ronald Cools; Frances Y. Kuo; Dirk Nuyens (SIAM J. Sci. Comput., 2006)

Constructing lattice rules based on weighted degree of exactness and worst case error. - Ronald Cools; Frances Y. Kuo; Dirk Nuyens (Computing, 2010)

Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications. - Ivan G. Graham; Frances Y. Kuo; Dirk Nuyens; Robert Scheichl; Ian H. Sloan (J. Comput. Phys., 2011)

Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. - Jan Baldeaux; Josef Dick; Gunther Leobacher; Dirk Nuyens; Friedrich Pillichshammer (Numer. Algorithms, 2012)

Weighted compound integration rules with higher order convergence for all N. - Fred J. Hickernell; Peter Kritzer; Frances Y. Kuo; Dirk Nuyens (Numer. Algorithms, 2012)

Conditional Sampling for Barrier Option Pricing under the LT Method. - Nico Achtsis; Ronald Cools; Dirk Nuyens (SIAM J. Financial Math., 2013)

The construction of good lattice rules and polynomial lattice rules. - Dirk Nuyens (Uniform Distribution and Quasi-Monte Carlo Methods, 2014)

Lattice rules for nonperiodic smooth integrands. - Josef Dick; Dirk Nuyens; Friedrich Pillichshammer (Numerische Mathematik, 2014)

Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs. - Josef Dick; Frances Y. Kuo; Quoc Thong Le Gia; Dirk Nuyens; Christoph Schwab (SIAM J. Numer. Anal., 2014)

Rank-1 lattice rules for multivariate integration in spaces of permutation-invariant functions - Error bounds and tractability. - Dirk Nuyens; Gowri Suryanarayana; Markus Weimar (Adv. Comput. Math., 2016)

Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation. - Frances Y. Kuo; Dirk Nuyens (Found. Comput. Math., 2016)

Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions. - Ronald Cools; Frances Y. Kuo; Dirk Nuyens; Gowri Suryanarayana (J. Complex., 2016)

Infinite-dimensional integration and the multivariate decomposition method. - Frances Y. Kuo; Dirk Nuyens; Leszek Plaskota; Ian H. Sloan; Grzegorz W. Wasilkowski (J. Comput. Appl. Math., 2017)

Multivariate integration over Rs with exponential rate of convergence. - Dong T. P. Nguyen; Dirk Nuyens (J. Comput. Appl. Math., 2017)

A Multi-Index Quasi-Monte Carlo Algorithm for Lognormal Diffusion Problems. - Pieterjan Robbe; Dirk Nuyens; Stefan Vandewalle (SIAM J. Sci. Comput., 2017)

Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. - Ivan G. Graham; Frances Y. Kuo; Dirk Nuyens; Robert Scheichl; Ian H. Sloan (Numerische Mathematik, 2018)

Analysis of Circulant Embedding Methods for Sampling Stationary Random Fields. - Ivan G. Graham; Frances Y. Kuo; Dirk Nuyens; Robert Scheichl; Ian H. Sloan (SIAM J. Numer. Anal., 2018)

Efficient Implementations of the Multivariate Decomposition Method for Approximating Infinite-Variate Integrals. - Alexander D. Gilbert; Frances Y. Kuo; Dirk Nuyens; Grzegorz W. Wasilkowski (SIAM J. Sci. Comput., 2018)

Enhanced Multi-Index Monte Carlo by means of Multiple Semi-Coarsened Multigrid for Anisotropic Diffusion Problems. - Pieterjan Robbe; Dirk Nuyens; Stefan Vandewalle (CoRR, 2019)

Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters. - Ronald Cools; Frances Y. Kuo; Dirk Nuyens; Ian H. Sloan (CoRR, 2019)

Lattice rules with random n achieve nearly the optimal O(n-α-1∕2) error independently of the dimension. - Peter Kritzer; Frances Y. Kuo; Dirk Nuyens; Mario Ullrich (J. Approx. Theory, 2019)

Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications. - Tianfeng Hou; Dirk Nuyens; Staf Roels; Hans Janssen (Reliab. Eng. Syst. Saf., 2019)

Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method. - Pieterjan Robbe; Dirk Nuyens; Stefan Vandewalle (SIAM J. Sci. Comput., 2019)

Strang Splitting in Combination with Rank-1 and Rank-r Lattices for the Time-Dependent Schrödinger Equation. - Yuya Suzuki; Gowri Suryanarayana; Dirk Nuyens (SIAM J. Sci. Comput., 2019)

Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters. - Ronald Cools; Frances Y. Kuo; Dirk Nuyens; Ian H. Sloan (75 Years of Mathematics of Computation, 2020)

Scaled lattice rules for integration on Rd achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces. - Dirk Nuyens; Yuya Suzuki (CoRR, 2021)

Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness. - Adrian Ebert; Peter Kritzer; Dirk Nuyens; Onyekachi Osisiogu (J. Complex., 2021)

Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory. - Tobias Hartung; Karl Jansen; Frances Y. Kuo; Hernan Leövey; Dirk Nuyens; Ian H. Sloan (J. Comput. Phys., 2021)

Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights. - Ronald Cools; Frances Y. Kuo; Dirk Nuyens; Ian H. Sloan (Math. Comput., 2021)

Function integration, reconstruction and approximation using rank-1 lattices. - Frances Y. Kuo; Giovanni Migliorati; Fabio Nobile; Dirk Nuyens (Math. Comput., 2021)

Enhanced multi-index Monte Carlo by means of multiple semicoarsened multigrid for anisotropic diffusion problems. - Pieterjan Robbe; Dirk Nuyens; Stefan Vandewalle (Numer. Linear Algebra Appl., 2021)

MDFEM: Multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM. - Dong T. P. Nguyen; Dirk Nuyens (Numerische Mathematik, 2021)

Constructing Embedded Lattice-based Algorithms for Multivariate Function Approximation with a Composite Number of Points. - Frances Y. Kuo; Weiwen Mo; Dirk Nuyens (CoRR, 2022)

Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces. - Dirk Nuyens; Yuya Suzuki (Math. Comput., 2022)

Comparison of Two Search Criteria for Lattice-based Kernel Approximation. - Frances Y. Kuo; Weiwen Mo; Dirk Nuyens; Ian H. Sloan; Abirami Srikumar (CoRR, 2023)

A randomised lattice rule algorithm with pre-determined generating vector and random number of points for Korobov spaces with 0 < α≤ 1/2. - Dirk Nuyens; Laurence Wilkes (CoRR, 2023)

Random-prime-fixed-vector randomised lattice-based algorithm for high-dimensional integration. - Frances Y. Kuo; Dirk Nuyens; Laurence Wilkes (J. Complex., 2023)

Quasi-Monte Carlo methods for uncertainty quantification of wave propagation and scattering problems modelled by the Helmholtz equation. - Ivan G. Graham; Frances Y. Kuo; Dirk Nuyens; Ian H. Sloan; Euan A. Spence (CoRR, 2025)

Regularity and Tailored Regularization of Deep Neural Networks, with application to parametric PDEs in uncertainty quantification. - Alexander Keller 001; Frances Y. Kuo; Dirk Nuyens; Ian H. Sloan (CoRR, 2025)

Modeling Scrap Composition in Electric Arc and Basic Oxygen Furnaces. - Yiqing Zhou; Karsten Naert; Dirk Nuyens (CoRR, 2025)

Sensitivity Analysis of State Space Models for Scrap Composition Estimation in EAF and BOF. - Yiqing Zhou; Karsten Naert; Dirk Nuyens (CoRR, 2025)

Error bounds for function approximation using generated sets. - Ronald Cools; Dirk Nuyens; Laurence Wilkes (CoRR, 2025)

A localized consensus-based sampling algorithm. - Arne Bouillon; Alexander Bodard; Panagiotis Patrinos; Dirk Nuyens; Giovanni Samaey (CoRR, 2025)