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Discrepancy Theory and Quasi-Monte Carlo Integration [chapter]

Josef Dick, Friedrich Pillichshammer
2014 Lecture notes in mathematics  
Discrepancy theory was established as an area of research going back to the seminal paper by Weyl (1916), whereas Monte Carlo (and later quasi-Monte Carlo) was invented in the 1940s by John von Neumann  ...  Discrepancy theory was established as an area of research going back to the seminal paper by Weyl (1916), whereas Monte Carlo (and later quasi-Monte Carlo) was invented in the 1940s by John von Neumann  ...  The authors thank Michaela Szölgyenyi and Henryk Woźniakowski for many helpful suggestions.  ... 
doi:10.1007/978-3-319-04696-9_9 fatcat:nnsunrh7uzarfaathtskvh7tme

A Comparison of Popular Point Configurations on S^2 [article]

D.P. Hardin, T. J. Michaels, E.B. Saff
2016 arXiv   pre-print
There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis.  ...  We analyze numerically the leading order asymptotics for the Riesz and logarithmic potential energy for these configurations with total points N<50,000 and present some new conjectures.  ...  Determining an exact minimal configuration for a fixed N and s is a highly nonlinear optimization problem.  ... 
arXiv:1607.04590v3 fatcat:m6pxw5f22ngmjm5qzqum5aux74

Information-based complexity

1989 Mathematics and Computers in Simulation  
> where n = ©(e'^loge-1)^-1^2), and the points x¡ are derived from Hammersley points.  ...  Rabin [72] studied the class A2 for the exact solution of linear systems, e = 0, and for an arbitrary nonsingular matrix A.  ... 
doi:10.1016/0378-4754(89)90072-4 fatcat:unyblw2m7zdithdyelkwxlsoim

Information-based complexity

Edward W. Packel, J. F. Traub
1987 Nature  
> where n = ©(e'^loge-1)^-1^2), and the points x¡ are derived from Hammersley points.  ...  Rabin [72] studied the class A2 for the exact solution of linear systems, e = 0, and for an arbitrary nonsingular matrix A.  ... 
doi:10.1038/328029a0 fatcat:p55xu6essbgxjerpf2w37lyck4

Perspectives on Information-Based Complexity

J. F. Traub, H. Wo\'zniakowski
1992 Bulletin of the American Mathematical Society  
> where n = ©(e'^loge-1)^-1^2), and the points x¡ are derived from Hammersley points.  ...  Rabin [72] studied the class A2 for the exact solution of linear systems, e = 0, and for an arbitrary nonsingular matrix A.  ... 
doi:10.1090/s0273-0979-1992-00240-9 fatcat:cg6dj5jfmfadjdu4kxzguasd24

Information-Based Complexity

1989 Science  
> where n = ©(e'^loge-1)^-1^2), and the points x¡ are derived from Hammersley points.  ...  Rabin [72] studied the class A2 for the exact solution of linear systems, e = 0, and for an arbitrary nonsingular matrix A.  ... 
doi:10.1126/science.243.4895.1142-a pmid:17799891 fatcat:yt5qwb6sqjg4lhyqoicfre5oyi

Information-Based Complexity

H Wozniakowski
1986 Annual Review of Computer Science  
> where n = ©(e'^loge-1)^-1^2), and the points x¡ are derived from Hammersley points.  ...  Rabin [72] studied the class A2 for the exact solution of linear systems, e = 0, and for an arbitrary nonsingular matrix A.  ... 
doi:10.1146/annurev.cs.01.060186.001535 fatcat:a7ogeqrrdbaunnqdjmcnjvx3uq

DiceDesignandDiceEval: TwoRPackages for Design and Analysis of Computer Experiments

Delphine Dupuy, Céline Helbert, Jessica Franco
2015 Journal of Statistical Software  
A two-dimensional test function will be a running example to illustrate the main functionalities of these packages and an industrial case study in five dimensions will also be detailed.  ...  Package DiceEval deals with the fit, the validation and the comparison of metamodels. After a brief presentation of the context, we focus on the architecture of these two packages.  ...  We also wish to thank the anonymous referees for several helpful comments and suggestions that improved and clarified the presentation of this work.  ... 
doi:10.18637/jss.v065.i11 fatcat:ndukgtjzh5db5c4z33f4vnbsay

Recent Mathematical Tables

1953 Mathematics of Computation  
The table can be used to find the exact number of lattice points inside or on a circle of radius r by means of the formula for positive k < 100.  ...  The author provides a table for the power of the C test to 2D against this alternative (under the assumption again of exact normality) at the 95% level for p = .  ...  But nevertheless, this restriction will make the table unsuitable for calculations of gas flow at higher temperatures, such as the flow in high pressure compressors and gas turbines.  ... 
doi:10.1090/s0025-5718-53-99370-3 fatcat:wtg7ywqdvrap3agzkmam5wtvcq

Localized Bases for Kernel Spaces on the Unit Sphere

E. Fuselier, T. Hangelbroek, F. J. Narcowich, J. D. Ward, G. B. Wright
2013 SIAM Journal on Numerical Analysis  
For a set of N scattered sites, the standard basis for such a space utilizes N globally supported kernels; computing with it is prohibitively expensive for large N.  ...  Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central  ...  quasi-uniform icosahadedral and the low discrepancy Hammersley families of nodes on the sphere.  ... 
doi:10.1137/120876940 fatcat:fzhzc62zg5hy5ask4qxd2x227a

Living on the Edge: An Unified Approach to Antithetic Sampling [article]

Roberto Casarin, Radu V. Craiu, Lorenzo Frattarolo, Christian P. Robert
2021 arXiv   pre-print
This perspective enables the derivation of new properties of the sampling schemes: i) optimality in the Kullback-Leibler sense; ii) closed-form multivariate Kendall's τ and Spearman's ρ; iii)ranking in  ...  We introduce a new class of antithetic schemes that includes the most used antithetic proposals.  ...  On the l2 -discrepancy for anchored boxes. Journal of Complexity, 14(4):527–556. McKay, M. D., Beckman, R. J., and Conover, W. J. (1979).  ... 
arXiv:2110.15124v2 fatcat:r6jhddsdx5cxxh3m22zn3z7edm

Percolation, statistical topography, and transport in random media

M. B. Isichenko
1992 Reviews of Modern Physics  
For rapidly decaying correlations of g, the isopotentials fall into the same universality class as the perimeters of percolation clusters.  ...  A review of classical percolation theory is presented, with an emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media.  ...  For the case of a symmetric distribution of g(x; ), they related the exact critical level h, = 0 to the exact critical probability p, (T, s)= -, ' (see Table II ).  ... 
doi:10.1103/revmodphys.64.961 fatcat:6h7jksi7wncu5cixnqxcglzrne

Conformal invariance in two-dimensional percolation [article]

Robert Langlands, Philippe Pouliot, Yvan Saint-Aubin
1994 arXiv   pre-print
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique  ...  On the other hand, one ulterior purpose is to draw the attention of mathematicians to the mathematical problems posed by the physical notions.  ...  As we saw, both artifices have limitations (See §3.5 and §3.6.) that could cause the discrepancy between the value of π(H) for S 1 and S 2 , as well as the discrepancy of .024 betweenπ(H) andπ(0) that  ... 
arXiv:math/9401222v1 fatcat:ip6vgqimrjb7dfweczvv3gcpka

Hyperbolic Cross Approximation [article]

Dinh Dũng, Vladimir N. Temlyakov, Tino Ullrich
2017 arXiv   pre-print
The theory of hyperbolic cross approximation and related theory of functions with mixed smoothness are under detailed study for more than 50 years.  ...  This and recently discovered deep connections between the hyperbolic cross approximation (and related sparse grids) and other areas of mathematics such as probability, discrepancy, and numerical integration  ...  The authors acknowledge the fruitful discussions with D.B. Bazarkhanov,  ... 
arXiv:1601.03978v3 fatcat:awkabqxvqva3xgsk5tqo5vugqq

Algebraic statistics

Seth Sullivant
2012 Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12  
To test whether a given data set is consistent with the model of Hardy-Weinberg equilibrium, we need to perform an exact test.  ...  The set of partially symmetric matrices with rank ≤ k is an irreducible variety, defined by the vanishing of all (k + 1) × (k + 1) subdeterminants.  ...  For instance, in the case of the factor analysis model from Example 13.2.3 all the generators of the ideal I G that are lists are homogeneous with respect to the upstream grading.  ... 
doi:10.1145/2442829.2442835 dblp:conf/issac/Sullivant12 fatcat:gcmhfgalwveifi2h4rug2afgga
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