## Hickernell, Fred J.

Compute Distance To:
 Author ID: hickernell.fred-j Published as: Hickernell, Fred J.; Hickernell, F. J.; Hickernell, Fred more...less External Links: MGP
 Documents Indexed: 97 Publications since 1983 3 Contributions as Editor Co-Authors: 69 Co-Authors with 85 Joint Publications 2,211 Co-Co-Authors
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### Co-Authors

 15 single-authored 10 Yue, Rongxian 8 Woźniakowski, Henryk 6 Hong, Hee Sun 5 Fang, Kai-Tai 5 Jiménez Rugama, Lluís Antoni 5 Sloan, Ian Hugh 5 Wasilkowski, Grzegorz W. 4 Fasshauer, Gregory E. 4 Kritzer, Peter 4 Liu, Min-Qian 4 Zeng, Xiaoyan 3 An, Hongzhi 3 Ding, Yuhan 3 Liang, Jiajuan 3 Niu, Ben 3 Zhu, Lixing 2 Ai, Mingyao 2 Dick, Josef 2 Heinrich, Stefan 2 Jagadeeswaran, R. 2 Lemieux, Christiane 2 Li, Runze 2 Li, Yiou 2 Liu, Kwong-Ip 2 Müller-Gronbach, Thomas 2 Niederreiter, Harald 2 Owen, Art B. 2 Ritter, Klaus 2 Song, Guohui 2 Wang, Xiaoqun 2 Yang, Shijun 2 Yortsos, Yannis C. 1 Anitescu, Mihai 1 Arnaud, Elise 1 Chen, Jiading 1 Choi, Sou-Cheng T. 1 Clancy, Nicholas 1 Damelin, Steven Benjamin 1 Fang, Gensun 1 Feng, Keqin 1 Gilquin, Laurent 1 Hamilton, Caleb 1 Hon, Yiu-Chung 1 Jiang, Lan 1 Kuo, Frances Y. 1 L’Ecuyer, Pierre 1 Leung, King-Tai 1 Li, Da 1 Li, Dong 1 Li, Huan 1 Lin, Dennis Kon Jin 1 Liu, Xin 1 Liu, Yuewei 1 Monod, Hervé 1 Nuyens, Dirk 1 Prieur, Clémentine 1 Ragozin, David L. 1 Riddle, John 1 Roderick, Oleg 1 Tong, Xin 1 Wang, Yuan 1 Wasilkowski, Greg 1 Wei, Bocheng 1 Wei, Gang 1 Xu, Lanju 1 Ye, Qi 1 Zhang, Haizhang 1 Zhang, Yizhi 1 Zhou, Xuan
all top 5

### Serials

 12 Journal of Complexity 9 Mathematics of Computation 5 SIAM Journal on Numerical Analysis 5 Statistica Sinica 4 Studies in Applied Mathematics 2 Metrika 2 Statistics & Probability Letters 2 Statistical Science 2 Science in China. Series A 2 Applied and Computational Harmonic Analysis 2 Advances in Computational Mathematics 2 International Journal of Numerical Analysis and Modeling 1 Journal of Fluid Mechanics 1 ACM Transactions on Mathematical Software 1 Annals of the Institute of Statistical Mathematics 1 Applied Mathematics and Computation 1 Biometrika 1 Journal of Computational and Applied Mathematics 1 Journal of Multivariate Analysis 1 Journal of Statistical Planning and Inference 1 Mathematics and Computers in Simulation 1 Chinese Annals of Mathematics. Series A 1 Constructive Approximation 1 Mathematical and Computer Modelling 1 Numerical Algorithms 1 SIAM Journal on Applied Mathematics 1 Chinese Science Bulletin 1 SIAM Journal on Scientific Computing 1 Finite Fields and their Applications 1 The Journal of Fourier Analysis and Applications 1 ACM Transactions on Modeling and Computer Simulation 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Radon Series on Computational and Applied Mathematics 1 Communication on Applied Mathematics and Computation 1 Statistics and Computing 1 International Journal for Uncertainty Quantification
all top 5

### Fields

 67 Numerical analysis (65-XX) 30 Statistics (62-XX) 21 Approximations and expansions (41-XX) 13 Number theory (11-XX) 7 Functional analysis (46-XX) 6 Computer science (68-XX) 6 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Probability theory and stochastic processes (60-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

87 Publications have been cited 1,327 times in 767 Documents Cited by Year
A generalized discrepancy and quadrature error bound. Zbl 0889.41025
Hickernell, Fred J.
1998
Lattice rules: How well do they measure up? Zbl 0920.65010
Hickernell, Fred J.
1998
Uniform designs limit aliasing. Zbl 1036.62060
Hickernell, Fred J.; Liu, Min-Qian
2002
Integration and approximation in arbitrary dimensions. Zbl 0939.41004
Hickernell, F. J.; Wozniakowski, H.
2000
Connections among different criteria for asymmetrical fractional factorial designs. Zbl 1109.62069
Liu, Min-Qian; Fang, Kai-Tai; Hickernell, Fred J.
2006
Multi-level Monte Carlo algorithms for infinite-dimensional integration on $$\mathbb R^{\mathbb N}$$. Zbl 1207.65005
Hickernell, Fred J.; Müller-Gronbach, Thomas; Niu, Ben; Ritter, Klaus
2010
The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension. Zbl 1032.65006
Hickernell, Fred J.; Wang, Xiaoqun
2002
Algorithm 823: Implementing scrambled digital sequences. Zbl 1068.11049
Hong, Hee Sun; Hickernell, Fred J.
2003
Randomized Halton sequences. Zbl 0965.65005
Wang, X.; Hickernell, F. J.
2000
The mean square discrepancy of randomized nets. Zbl 0887.65030
Hickernell, Fred J.
1996
The existence of good extensible rank-1 lattices. Zbl 1029.65004
Hickernell, Fred J.; Niederreiter, Harald
2003
Obtaining O$$(N^{-2+\varepsilon})$$ convergence for lattice quadrature rules. Zbl 1002.65009
Hickernell, Fred J.
2002
The mean square discrepancy of scrambled $$(t,s)$$-sequences. Zbl 1049.65005
Hickernell, Fred J.; Yue, Rong-Xian
2000
Linear stability of miscible displacement processes in porous media in the absence of dispersion. Zbl 0603.76091
Hickernell, F. J.; Yortsos, Y. C.
1986
On tractability of weighted integration over bounded and unbounded regions in $$\mathbb{R}^s$$. Zbl 1068.65005
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
Time-dependent critical layers in shear flows on the beta-plane. Zbl 0561.76056
Hickernell, Fred J.
1984
Testing multivariate uniformity and its applications. Zbl 0958.65016
Liang, Jia-Juan; Fang, Kai-Tai; Hickernell, Fred J.; Li, Runze
2001
Goodness-of-fit statistics, discrepancies and robust designs. Zbl 0940.62067
Hickernell, Fred J.
1999
Quadrature error bounds with applications to lattice rules. Zbl 0855.41024
Hickernell, Fred J.
1996
Trigonometric spectral collocation methods on lattices. Zbl 1036.65093
Li, Dong; Hickernell, Fred J.
2003
$$E(s^2)$$-optimality and minimum discrepancy in 2-level supersaturated designs. Zbl 1002.62059
Liu, Min-Qian; Hickernell, Fred J.
2002
Extensible lattice sequences for quasi-Monte Carlo quadrature. Zbl 0974.65004
Hickernell, Fred J.; Hong, Hee Sun; L’Écuyer, Pierre; Lemieux, Christiane
2000
Deterministic multi-level algorithms for infinite-dimensional integration on $$\mathbb R^{\mathbb N}$$. Zbl 1218.65005
Niu, Ben; Hickernell, Fred J.; Müller-Gronbach, Thomas; Ritter, Klaus
2011
Tractability of multivariate integration for periodic functions. Zbl 1006.65023
Hickernell, Fred J.; Woźniakowski, Henryk
2001
On dimension-independent rates of convergence for function approximation with Gaussian kernels. Zbl 1243.65025
Fasshauer, Gregory E.; Hickernell, Fred J.; Woźniakowski, Henryk
2012
Reproducing kernel Banach spaces with the $$\ell^1$$ norm. Zbl 1269.46020
Song, Guohui; Zhang, Haizhang; Hickernell, Fred J.
2013
Monte Carlo simulation of stochastic integrals when the cost of function evaluation is dimension dependent. Zbl 1182.91205
Niu, Ben; Hickernell, Fred J.
2009
Robust designs for fitting linear models with misspecification. Zbl 0940.62071
Yue, Rong-Xian; Hickernell, Fred J.
1999
Solving support vector machines in reproducing kernel Banach spaces with positive definite functions. Zbl 1366.68236
Fasshauer, Gregory E.; Hickernell, Fred J.; Ye, Qi
2015
Control variates for quasi-Monte Carlo (with comments and rejoinder). Zbl 1100.65006
Hickernell, Fred J.; Lemieux, Christiane; Owen, Art B.
2005
What affects the accuracy of quasi-Monte Carlo quadrature? Zbl 0941.65025
Hickernell, Fred J.
2000
On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space. Zbl 1292.49041
Damelin, S. B.; Hickernell, F. J.; Ragozin, D. L.; Zeng, X.
2010
Multivariate interpolation with increasingly flat radial basis functions of finite smoothness. Zbl 1250.41002
Song, Guohui; Riddle, John; Fasshauer, Gregory E.; Hickernell, Fred J.
2012
The discrepancy and gain coefficients of scrambled digital nets. Zbl 1114.11306
Yue, Rong-Xian; Hickernell, Fred J.
2002
The asymptotic efficiency of randomized nets for quadrature. Zbl 1043.65051
Hickernell, Fred J.; Hong, Hee Sun
1999
Optimal quadrature for Haar wavelet spaces. Zbl 1035.65004
Heinrich, Stefan; Hickernell, Fred J.; Yue, Rong-Xian
2004
Radial basis function approximations as smoothing splines. Zbl 0927.41008
Hickernell, Fred J.; Hon, Y. C.
1999
On tractability of weighted integration for certain Banach spaces of functions. Zbl 1041.65006
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
Tractability of linear multivariate problems in the average case setting. Zbl 1141.65335
Hickernell, Fred; Wasilkowski, Greg; Woźniakowski, Henryk
2008
The price of pessimism for multidimensional quadrature. Zbl 1006.65022
Hickernell, Fred J.; Woźniakowski, Henryk
2001
Linear error-block codes. Zbl 1156.94433
Feng, Keqin; Xu, Lanju; Hickernell, Fred J.
2006
Error analysis of splines for periodic problems using lattice designs. Zbl 1097.65027
Zeng, Xiaoyan; Leung, King-Tai; Hickernell, Fred J.
2006
On strong tractability of weighted multivariate integration. Zbl 1071.41027
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
My dream quadrature rule. Zbl 1024.65024
Hickernell, Fred J.
2003
Optimality criteria for multiresponse linear models based on predictive ellipsoids. Zbl 1206.62137
Liu, Xin; Yue, Rong-Xian; Hickernell, Fred J.
2011
Some necessary uniform tests for spherical symmetry. Zbl 1169.62052
Liang, Jiajuan; Fang, Kai-Tai; Hickernell, Fred J.
2008
Computing multivariate normal probabilities using rank-1 lattice sequences. Zbl 0922.65099
Hickernell, Fred J.; Hong, Hee Sun
1998
Linear stability of immiscible displacement in porous media. Zbl 0669.76124
Yortsos, Y. C.; Hickernell, F. J.
1989
Orthogonal bases for polynomial regression with derivative information in uncertainty quantification. Zbl 1291.65188
Li, Yiou; Anitescu, Mihai; Roderick, Oleg; Hickernell, Fred
2011
The cost of deterministic, adaptive, automatic algorithms: cones, not balls. Zbl 1294.65032
Clancy, Nicholas; Ding, Yuhan; Hamilton, Caleb; Hickernell, Fred J.; Zhang, Yizhi
2014
The strong tractability of multivariate integration using lattice rules. Zbl 1042.65004
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
A piecewise constant algorithm for weighted $$L_{1}$$ approximation over bounded or unbounded regions in $$\mathbb R^s$$. Zbl 1103.65018
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2005
Reliable adaptive cubature using digital sequences. Zbl 1356.65006
Hickernell, Fred J.; Jiménez Rugama, Lluís Antoni
2016
Weighted compound integration rules with higher order convergence for all $$N$$. Zbl 1240.65002
Hickernell, Fred J.; Kritzer, Peter; Kuo, Frances Y.; Nuyens, Dirk
2012
Average case approximation: convergence and tractability of Gaussian kernels. Zbl 1271.65028
Fasshauer, G. E.; Hickernell, F. J.; Woźniakowski, H.
2012
Spline methods using integration lattices and digital nets. Zbl 1184.41009
Zeng, Xiaoyan; Kritzer, Peter; Hickernell, Fred J.
2009
Approximation on anisotropic Besov classes with mixed norms by standard information. Zbl 1078.41027
Fang, Gensun; Hickernell, Fred J.; Li, Huan
2005
Adaptive multidimensional integration based on rank-1 lattices. Zbl 1356.65008
Jiménez Rugama, Lluís Antoni; Hickernell, Fred J.
2016
The evolution of large-horizontal-scale disturbances in marginally stable, inviscid, shear flows. I: Derivation of the amplitude evolution equations. Zbl 0531.76052
Hickernell, Fred J.
1983
Optimal foldover plans for regular $$s$$-level fractional factorial designs. Zbl 1136.62051
Ai, Mingyao; Hickernell, Fred J.; Lin, Dennis K. J.
2008
An historical overview of lattice point sets. Zbl 1012.11067
Wang, Yuan; Hickernell, Fred J.
2002
The distribution of the discrepancy of scrambled digital ($$t$$,$$m$$,$$s$$)-nets. Zbl 1020.65009
Hong, Hee Sun; Hickernell, Fred J.; Wei, Gang
2003
Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling. Zbl 1302.65007
Hickernell, Fred J.; Jiang, Lan; Liu, Yuewei; Owen, Art B.
2013
Quasi-Monte Carlo methods and their randomizations. Zbl 1007.65003
Hickernell, Fred J.; Hong, Hee Sun
2002
Strong tractability of integration using scrambled Niederreiter points. Zbl 1079.65011
Yue, Rong-Xian; Hickernell, Fred J.
2005
Monte Carlo and quasi-Monte Carlo methods 2000. Proceedings of a conference, held at Hong Kong Baptist Univ., Hong Kong SAR, China, November 27 – December 1, 2000. Zbl 0980.00040
2002
A new class of consistent estimators for stochastic linear regressive models. Zbl 0884.62095
An, Hongzhi; Hickernell, Fred J.; Zhu, Lixing
1997
Local adaption for approximation and minimization of univariate functions. Zbl 1365.65032
Choi, Sou-Cheng T.; Ding, Yuhan; Hickernell, Fred J.; Tong, Xin
2017
The evolution of large-horizontal-scale disturbances in marginally stable, inviscid, shear flows. II: Solutions of the Bouissinesq equation. Zbl 0531.76053
Hickernell, Fred J.
1983
Integration and approximation based on scramble sampling in arbitrary dimensions. Zbl 0995.65005
Yue, Rong-Xian; Hickernell, Fred J.
2001
Iterative construction of replicated designs based on Sobol’ sequences. (Construction de plans répliqués à partir de séquences de Sobol’.) Zbl 1355.65009
Gilquin, Laurent; Jiménez Rugama, Lluís Antoni; Arnaud, Élise; Hickernell, Fred J.; Monod, Hervé; Prieur, Clémentine
2017
A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017
Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J.
2009
A comparison of random and quasirandom points for multidimensional quadrature. Zbl 0831.65023
Hickernell, Fred J.
1995
Fast automatic Bayesian cubature using lattice sampling. Zbl 1435.62028
2019
The relationship between discrepancies defined on a domain and on its subset. Zbl 1094.62094
Liu, Min-Qian; Hickernell, Fred J.
2006
Strong tractability of quasi-Monte Carlo quadrature using nets for certain Banach spaces. Zbl 1129.65003
Yue, Rong-Xian; Hickernell, Fred J.
2006
An upper bound on the growth rate of a linear instability in a homogeneous shear flow. Zbl 0588.76068
Hickernell, Fred J.
1985
Simplified analytical expressions for numerical differentiation via cycle index. Zbl 1159.65027
Hickernell, Fred J.; Yang, Shijun
2009
Explicit Hermite interpolation polynomials via the cycle index applications. Zbl 1162.65004
Hickernell, Fred J.; Yang, Shijun
2008
A class of asymptotically optimal sequential tests for composite hypotheses. Zbl 0812.62084
1994
A goodness-of-fit test for linearity of a stochastic regression model. Zbl 0898.62057
Zhu, Lixing; Hickernell, F. J.; An, Hongzhi
1997
Designs for smoothing spline ANOVA models. Zbl 1320.62187
Yue, Rong-Xian; Hickernell, F. J.
2002
Regression transformation diagnostics for explanatory variables. Zbl 0881.62078
Wei, Bo-Cheng; Hickernell, Fred J.
1996
Exponential tractability of linear tensor product problems. Zbl 07240864
Hickernell, Fred J.; Kritzer, Peter; Woźniakowski, Henryk
2020
Adaptive quasi-Monte Carlo methods for cubature. Zbl 1405.65011
Hickernell, Fred J.; Jiménez Rugama, Lluís Antoni; Li, Da
2018
An algorithm-driven approach to error analysis for multidimensional integration. Zbl 1131.41316
Hickernell, Fred J.; Dick, Josef
2008
Universal optimality of digital nets and lattice designs. Zbl 1178.62080
Ai, MingYao; Hickernell, Fred J.
2009
Exponential tractability of linear tensor product problems. Zbl 07240864
Hickernell, Fred J.; Kritzer, Peter; Woźniakowski, Henryk
2020
Fast automatic Bayesian cubature using lattice sampling. Zbl 1435.62028
2019
Adaptive quasi-Monte Carlo methods for cubature. Zbl 1405.65011
Hickernell, Fred J.; Jiménez Rugama, Lluís Antoni; Li, Da
2018
Local adaption for approximation and minimization of univariate functions. Zbl 1365.65032
Choi, Sou-Cheng T.; Ding, Yuhan; Hickernell, Fred J.; Tong, Xin
2017
Iterative construction of replicated designs based on Sobol’ sequences. (Construction de plans répliqués à partir de séquences de Sobol’.) Zbl 1355.65009
Gilquin, Laurent; Jiménez Rugama, Lluís Antoni; Arnaud, Élise; Hickernell, Fred J.; Monod, Hervé; Prieur, Clémentine
2017
Reliable adaptive cubature using digital sequences. Zbl 1356.65006
Hickernell, Fred J.; Jiménez Rugama, Lluís Antoni
2016
Adaptive multidimensional integration based on rank-1 lattices. Zbl 1356.65008
Jiménez Rugama, Lluís Antoni; Hickernell, Fred J.
2016
Solving support vector machines in reproducing kernel Banach spaces with positive definite functions. Zbl 1366.68236
Fasshauer, Gregory E.; Hickernell, Fred J.; Ye, Qi
2015
The cost of deterministic, adaptive, automatic algorithms: cones, not balls. Zbl 1294.65032
Clancy, Nicholas; Ding, Yuhan; Hamilton, Caleb; Hickernell, Fred J.; Zhang, Yizhi
2014
Reproducing kernel Banach spaces with the $$\ell^1$$ norm. Zbl 1269.46020
Song, Guohui; Zhang, Haizhang; Hickernell, Fred J.
2013
Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling. Zbl 1302.65007
Hickernell, Fred J.; Jiang, Lan; Liu, Yuewei; Owen, Art B.
2013
On dimension-independent rates of convergence for function approximation with Gaussian kernels. Zbl 1243.65025
Fasshauer, Gregory E.; Hickernell, Fred J.; Woźniakowski, Henryk
2012
Multivariate interpolation with increasingly flat radial basis functions of finite smoothness. Zbl 1250.41002
Song, Guohui; Riddle, John; Fasshauer, Gregory E.; Hickernell, Fred J.
2012
Weighted compound integration rules with higher order convergence for all $$N$$. Zbl 1240.65002
Hickernell, Fred J.; Kritzer, Peter; Kuo, Frances Y.; Nuyens, Dirk
2012
Average case approximation: convergence and tractability of Gaussian kernels. Zbl 1271.65028
Fasshauer, G. E.; Hickernell, F. J.; Woźniakowski, H.
2012
Deterministic multi-level algorithms for infinite-dimensional integration on $$\mathbb R^{\mathbb N}$$. Zbl 1218.65005
Niu, Ben; Hickernell, Fred J.; Müller-Gronbach, Thomas; Ritter, Klaus
2011
Optimality criteria for multiresponse linear models based on predictive ellipsoids. Zbl 1206.62137
Liu, Xin; Yue, Rong-Xian; Hickernell, Fred J.
2011
Orthogonal bases for polynomial regression with derivative information in uncertainty quantification. Zbl 1291.65188
Li, Yiou; Anitescu, Mihai; Roderick, Oleg; Hickernell, Fred
2011
Multi-level Monte Carlo algorithms for infinite-dimensional integration on $$\mathbb R^{\mathbb N}$$. Zbl 1207.65005
Hickernell, Fred J.; Müller-Gronbach, Thomas; Niu, Ben; Ritter, Klaus
2010
On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space. Zbl 1292.49041
Damelin, S. B.; Hickernell, F. J.; Ragozin, D. L.; Zeng, X.
2010
Monte Carlo simulation of stochastic integrals when the cost of function evaluation is dimension dependent. Zbl 1182.91205
Niu, Ben; Hickernell, Fred J.
2009
Spline methods using integration lattices and digital nets. Zbl 1184.41009
Zeng, Xiaoyan; Kritzer, Peter; Hickernell, Fred J.
2009
A multivariate fast discrete Walsh transform with an application to function interpolation. Zbl 1200.42017
Liu, Kwong-Ip; Dick, Josef; Hickernell, Fred J.
2009
Simplified analytical expressions for numerical differentiation via cycle index. Zbl 1159.65027
Hickernell, Fred J.; Yang, Shijun
2009
Universal optimality of digital nets and lattice designs. Zbl 1178.62080
Ai, MingYao; Hickernell, Fred J.
2009
Tractability of linear multivariate problems in the average case setting. Zbl 1141.65335
Hickernell, Fred; Wasilkowski, Greg; Woźniakowski, Henryk
2008
Some necessary uniform tests for spherical symmetry. Zbl 1169.62052
Liang, Jiajuan; Fang, Kai-Tai; Hickernell, Fred J.
2008
Optimal foldover plans for regular $$s$$-level fractional factorial designs. Zbl 1136.62051
Ai, Mingyao; Hickernell, Fred J.; Lin, Dennis K. J.
2008
Explicit Hermite interpolation polynomials via the cycle index applications. Zbl 1162.65004
Hickernell, Fred J.; Yang, Shijun
2008
An algorithm-driven approach to error analysis for multidimensional integration. Zbl 1131.41316
Hickernell, Fred J.; Dick, Josef
2008
Connections among different criteria for asymmetrical fractional factorial designs. Zbl 1109.62069
Liu, Min-Qian; Fang, Kai-Tai; Hickernell, Fred J.
2006
Linear error-block codes. Zbl 1156.94433
Feng, Keqin; Xu, Lanju; Hickernell, Fred J.
2006
Error analysis of splines for periodic problems using lattice designs. Zbl 1097.65027
Zeng, Xiaoyan; Leung, King-Tai; Hickernell, Fred J.
2006
The relationship between discrepancies defined on a domain and on its subset. Zbl 1094.62094
Liu, Min-Qian; Hickernell, Fred J.
2006
Strong tractability of quasi-Monte Carlo quadrature using nets for certain Banach spaces. Zbl 1129.65003
Yue, Rong-Xian; Hickernell, Fred J.
2006
Control variates for quasi-Monte Carlo (with comments and rejoinder). Zbl 1100.65006
Hickernell, Fred J.; Lemieux, Christiane; Owen, Art B.
2005
A piecewise constant algorithm for weighted $$L_{1}$$ approximation over bounded or unbounded regions in $$\mathbb R^s$$. Zbl 1103.65018
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2005
Approximation on anisotropic Besov classes with mixed norms by standard information. Zbl 1078.41027
Fang, Gensun; Hickernell, Fred J.; Li, Huan
2005
Strong tractability of integration using scrambled Niederreiter points. Zbl 1079.65011
Yue, Rong-Xian; Hickernell, Fred J.
2005
On tractability of weighted integration over bounded and unbounded regions in $$\mathbb{R}^s$$. Zbl 1068.65005
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
Optimal quadrature for Haar wavelet spaces. Zbl 1035.65004
Heinrich, Stefan; Hickernell, Fred J.; Yue, Rong-Xian
2004
On tractability of weighted integration for certain Banach spaces of functions. Zbl 1041.65006
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
On strong tractability of weighted multivariate integration. Zbl 1071.41027
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
The strong tractability of multivariate integration using lattice rules. Zbl 1042.65004
Hickernell, Fred J.; Sloan, Ian H.; Wasilkowski, Grzegorz W.
2004
Algorithm 823: Implementing scrambled digital sequences. Zbl 1068.11049
Hong, Hee Sun; Hickernell, Fred J.
2003
The existence of good extensible rank-1 lattices. Zbl 1029.65004
Hickernell, Fred J.; Niederreiter, Harald
2003
Trigonometric spectral collocation methods on lattices. Zbl 1036.65093
Li, Dong; Hickernell, Fred J.
2003
My dream quadrature rule. Zbl 1024.65024
Hickernell, Fred J.
2003
The distribution of the discrepancy of scrambled digital ($$t$$,$$m$$,$$s$$)-nets. Zbl 1020.65009
Hong, Hee Sun; Hickernell, Fred J.; Wei, Gang
2003
Uniform designs limit aliasing. Zbl 1036.62060
Hickernell, Fred J.; Liu, Min-Qian
2002
The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension. Zbl 1032.65006
Hickernell, Fred J.; Wang, Xiaoqun
2002
Obtaining O$$(N^{-2+\varepsilon})$$ convergence for lattice quadrature rules. Zbl 1002.65009
Hickernell, Fred J.
2002
$$E(s^2)$$-optimality and minimum discrepancy in 2-level supersaturated designs. Zbl 1002.62059
Liu, Min-Qian; Hickernell, Fred J.
2002
The discrepancy and gain coefficients of scrambled digital nets. Zbl 1114.11306
Yue, Rong-Xian; Hickernell, Fred J.
2002
An historical overview of lattice point sets. Zbl 1012.11067
Wang, Yuan; Hickernell, Fred J.
2002
Quasi-Monte Carlo methods and their randomizations. Zbl 1007.65003
Hickernell, Fred J.; Hong, Hee Sun
2002
Monte Carlo and quasi-Monte Carlo methods 2000. Proceedings of a conference, held at Hong Kong Baptist Univ., Hong Kong SAR, China, November 27 – December 1, 2000. Zbl 0980.00040
2002
Designs for smoothing spline ANOVA models. Zbl 1320.62187
Yue, Rong-Xian; Hickernell, F. J.
2002
Testing multivariate uniformity and its applications. Zbl 0958.65016
Liang, Jia-Juan; Fang, Kai-Tai; Hickernell, Fred J.; Li, Runze
2001
Tractability of multivariate integration for periodic functions. Zbl 1006.65023
Hickernell, Fred J.; Woźniakowski, Henryk
2001
The price of pessimism for multidimensional quadrature. Zbl 1006.65022
Hickernell, Fred J.; Woźniakowski, Henryk
2001
Integration and approximation based on scramble sampling in arbitrary dimensions. Zbl 0995.65005
Yue, Rong-Xian; Hickernell, Fred J.
2001
Integration and approximation in arbitrary dimensions. Zbl 0939.41004
Hickernell, F. J.; Wozniakowski, H.
2000
Randomized Halton sequences. Zbl 0965.65005
Wang, X.; Hickernell, F. J.
2000
The mean square discrepancy of scrambled $$(t,s)$$-sequences. Zbl 1049.65005
Hickernell, Fred J.; Yue, Rong-Xian
2000
Extensible lattice sequences for quasi-Monte Carlo quadrature. Zbl 0974.65004
Hickernell, Fred J.; Hong, Hee Sun; L&rsquo;Écuyer, Pierre; Lemieux, Christiane
2000
What affects the accuracy of quasi-Monte Carlo quadrature? Zbl 0941.65025
Hickernell, Fred J.
2000
Goodness-of-fit statistics, discrepancies and robust designs. Zbl 0940.62067
Hickernell, Fred J.
1999
Robust designs for fitting linear models with misspecification. Zbl 0940.62071
Yue, Rong-Xian; Hickernell, Fred J.
1999
The asymptotic efficiency of randomized nets for quadrature. Zbl 1043.65051
Hickernell, Fred J.; Hong, Hee Sun
1999
Radial basis function approximations as smoothing splines. Zbl 0927.41008
Hickernell, Fred J.; Hon, Y. C.
1999
A generalized discrepancy and quadrature error bound. Zbl 0889.41025
Hickernell, Fred J.
1998
Lattice rules: How well do they measure up? Zbl 0920.65010
Hickernell, Fred J.
1998
Computing multivariate normal probabilities using rank-1 lattice sequences. Zbl 0922.65099
Hickernell, Fred J.; Hong, Hee Sun
1998
A new class of consistent estimators for stochastic linear regressive models. Zbl 0884.62095
An, Hongzhi; Hickernell, Fred J.; Zhu, Lixing
1997
A goodness-of-fit test for linearity of a stochastic regression model. Zbl 0898.62057
Zhu, Lixing; Hickernell, F. J.; An, Hongzhi
1997
The mean square discrepancy of randomized nets. Zbl 0887.65030
Hickernell, Fred J.
1996
Quadrature error bounds with applications to lattice rules. Zbl 0855.41024
Hickernell, Fred J.
1996
Regression transformation diagnostics for explanatory variables. Zbl 0881.62078
Wei, Bo-Cheng; Hickernell, Fred J.
1996
A comparison of random and quasirandom points for multidimensional quadrature. Zbl 0831.65023
Hickernell, Fred J.
1995
A class of asymptotically optimal sequential tests for composite hypotheses. Zbl 0812.62084
1994
Linear stability of immiscible displacement in porous media. Zbl 0669.76124
Yortsos, Y. C.; Hickernell, F. J.
1989
Linear stability of miscible displacement processes in porous media in the absence of dispersion. Zbl 0603.76091
Hickernell, F. J.; Yortsos, Y. C.
1986
An upper bound on the growth rate of a linear instability in a homogeneous shear flow. Zbl 0588.76068
Hickernell, Fred J.
1985
Time-dependent critical layers in shear flows on the beta-plane. Zbl 0561.76056
Hickernell, Fred J.
1984
The evolution of large-horizontal-scale disturbances in marginally stable, inviscid, shear flows. I: Derivation of the amplitude evolution equations. Zbl 0531.76052
Hickernell, Fred J.
1983
The evolution of large-horizontal-scale disturbances in marginally stable, inviscid, shear flows. II: Solutions of the Bouissinesq equation. Zbl 0531.76053
Hickernell, Fred J.
1983
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### Cited by 781 Authors

 48 Qin, Hong 42 Hickernell, Fred J. 37 Dick, Josef 37 Fang, Kai-Tai 37 Kuo, Frances Y. 36 Woźniakowski, Henryk 35 Liu, Min-Qian 35 Pillichshammer, Friedrich 34 Sloan, Ian Hugh 31 Wasilkowski, Grzegorz W. 23 Chatterjee, Kashinath 21 Elsawah, A. M. 21 Nuyens, Dirk 20 Yue, Rongxian 18 Gnewuch, Michael 18 Kritzer, Peter 17 Zhou, Yongdao 15 Ou, Zujun 13 Lin, Dennis Kon Jin 12 Owen, Art B. 12 Wang, Xiaoqun 11 Goda, Takashi 10 Ai, Mingyao 10 Cools, Ronald 10 Li, Hongyi 9 Lemieux, Christiane 9 Tang, Yu 9 Ye, Qi 8 Ning, Jianhui 8 Ökten, Giray 7 Hinrichs, Aicke 7 L’Ecuyer, Pierre 7 Niederreiter, Harald 7 Novak, Erich 7 Sun, Fasheng 7 Wang, Zhenghong 6 Kämmerer, Lutz 6 Liu, Xin 6 Ritter, Klaus 6 Volkmer, Toni 6 Zhang, Runchu 5 Brauchart, Johann S. 5 Goldstein, Marvin E. 5 Jiménez Rugama, Lluís Antoni 5 Leobacher, Gunther 5 Leovey, Hernan 5 Plaskota, Leszek 5 Sinescu, Vasile 5 Suryanarayana, Gowri 5 Waterhouse, Benjamin J. 5 Xu, Hongquan 4 Chen, Hao 4 Churilov, Semyon Mikhailovich 4 Dass, Bal Kishan 4 Dimov, Ivan Todor 4 Fasshauer, Gregory E. 4 Griebel, Michael 4 Huang, Hengzhen 4 Joe, Stephen 4 Karvonen, Toni 4 Khartov, Alekseĭ Andreevich 4 Leib, Stewart J. 4 Li, Runze 4 Liu, Kwong-Ip 4 Ma, Changxing 4 Potts, Daniel 4 Schwab, Christoph 4 Sharma, Namita 4 Suzuki, Kosuke 4 Tezuka, Shu 4 Todorov, Venelin 4 Verma, Rashmi 4 Winker, Peter 4 Xu, Guiqiao 4 Xu, Yuesheng 4 Yang, Jianfeng 4 Yang, Xue 4 Yoshiki, Takehito 4 Zhang, Aijun 4 Zhang, Haizhang 4 Zhou, Xiaodong 4 Zou, Na 3 Baldeaux, Jan 3 Berrendero, Jose Ramon 3 Chen, Xueping 3 Chi, Hongmei 3 Cuevas, Antonio 3 Ding, Yuhan 3 Doerr, Benjamin 3 Ebert, Adrian 3 Faure, Henri 3 Gou, Tingxun 3 Guo, Bing 3 Hefter, Mario 3 Henze, Norbert 3 Homsy, George M. 3 Jiang, Bochuan 3 Kacewicz, Bolesław Z. 3 Katsaounis, Tena I. 3 Ke, Xiao ...and 681 more Authors
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### Cited in 159 Serials

 129 Journal of Complexity 43 Mathematics of Computation 37 Journal of Statistical Planning and Inference 34 Statistics & Probability Letters 20 Statistical Papers 19 Journal of Computational and Applied Mathematics 18 Journal of Fluid Mechanics 15 Journal of Approximation Theory 14 Metrika 14 Communications in Statistics. Theory and Methods 13 Computational Statistics and Data Analysis 12 The Annals of Statistics 12 Numerische Mathematik 11 Numerical Algorithms 11 Physics of Fluids 10 Constructive Approximation 10 Advances in Computational Mathematics 9 Journal of Computational Physics 9 Foundations of Computational Mathematics 8 Monte Carlo Methods and Applications 7 Mathematics and Computers in Simulation 7 Statistics 6 SIAM Journal on Numerical Analysis 6 Acta Mathematicae Applicatae Sinica. English Series 6 Journal of the Korean Statistical Society 5 Journal of Multivariate Analysis 5 Studies in Applied Mathematics 5 Applied Numerical Mathematics 5 SIAM Journal on Scientific Computing 5 Finite Fields and their Applications 5 European Journal of Mechanics. B. Fluids 5 Journal of Systems Science and Complexity 5 Analysis and Applications (Singapore) 5 Journal of Statistical Theory and Practice 5 Electronic Journal of Statistics 5 SIAM/ASA Journal on Uncertainty Quantification 4 Computers & Mathematics with Applications 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Engineering Mathematics 4 Mathematical and Computer Modelling 4 Journal of Scientific Computing 4 Computational Statistics 4 Applied and Computational Harmonic Analysis 4 The Journal of Fourier Analysis and Applications 4 Journal of Applied Statistics 4 Science China. Mathematics 4 Statistics and Computing 3 Journal of Mathematical Analysis and Applications 3 Annals of the Institute of Statistical Mathematics 3 Applied Mathematics and Computation 3 BIT 3 Statistical Science 3 Neural Computation 3 Communications in Statistics. Simulation and Computation 3 Journal of Statistical Computation and Simulation 3 Applied Mathematics. Series B (English Edition) 3 Mathematical Foundations of Computing 2 Applicable Analysis 2 The Canadian Journal of Statistics 2 Computer Physics Communications 2 Discrete Mathematics 2 Geophysical and Astrophysical Fluid Dynamics 2 Physics of Fluids 2 Physics Reports 2 Wave Motion 2 Archiv der Mathematik 2 Biometrics 2 Computing 2 Functiones et Approximatio. Commentarii Mathematici 2 Information Sciences 2 International Journal for Numerical Methods in Engineering 2 Mathematics of Operations Research 2 Memoirs of the American Mathematical Society 2 Proceedings of the American Mathematical Society 2 Journal of Economic Dynamics & Control 2 SIAM Journal on Matrix Analysis and Applications 2 Science in China. Series A 2 Designs, Codes and Cryptography 2 Applied Mathematical Modelling 2 Mathematical Programming. Series A. Series B 2 Computational Optimization and Applications 2 Computational and Applied Mathematics 2 International Journal of Theoretical and Applied Finance 2 Methodology and Computing in Applied Probability 2 International Journal of Wavelets, Multiresolution and Information Processing 2 SIAM Journal on Mathematics of Data Science 1 Advances in Applied Probability 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Israel Journal of Mathematics 1 Physica A 1 Physics of Fluids, A 1 Bulletin of Mathematical Biology 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of the American Statistical Association 1 Journal of Applied Probability 1 Journal of Econometrics 1 Journal of Number Theory 1 Journal of Optimization Theory and Applications 1 Mathematische Nachrichten ...and 59 more Serials
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### Cited in 35 Fields

 386 Numerical analysis (65-XX) 281 Statistics (62-XX) 122 Approximations and expansions (41-XX) 104 Number theory (11-XX) 63 Fluid mechanics (76-XX) 62 Computer science (68-XX) 61 Functional analysis (46-XX) 52 Probability theory and stochastic processes (60-XX) 29 Combinatorics (05-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 25 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Information and communication theory, circuits (94-XX) 21 Operations research, mathematical programming (90-XX) 19 Partial differential equations (35-XX) 12 Geophysics (86-XX) 8 Operator theory (47-XX) 8 Quantum theory (81-XX) 7 Mechanics of deformable solids (74-XX) 7 Systems theory; control (93-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Biology and other natural sciences (92-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Real functions (26-XX) 4 Measure and integration (28-XX) 4 Potential theory (31-XX) 4 Ordinary differential equations (34-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Integral equations (45-XX) 2 Special functions (33-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX)