Search Results - "DICK, JOSEF"

Walsh Spaces Containing Smooth Functions and Quasi-Monte Carlo Rules of Arbitrary High Order by Dick, Josef

“…We define a Walsh space which contains all functions whose partial mixed derivatives up to order 6 ≥ 1 exist and have finite variation. In particular, for a…”
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Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm by Dick, Josef, Goda, Takashi

“…We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and…”
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Numerical integration of Hölder continuous, absolutely convergent Fourier, Fourier cosine, and Walsh series by Dick, Josef

“…We introduce quasi-Monte Carlo rules for the numerical integration of functions f defined on [0,1]s, s≥1, which satisfy the following properties: the Fourier,…”
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Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions by Dick, Josef

“…In this paper, we give explicit constructions of point sets in the s-dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate…”
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Construction of Interlaced Scrambled Polynomial Lattice Rules of Arbitrary High Order by Goda, Takashi, Dick, Josef

“…Higher order scrambled digital nets are randomized quasi-Monte Carlo rules which have recently been introduced by Dick (Ann Stat 39:1372–1398, 2011 ) and shown…”
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Random weights, robust lattice rules and the geometry of the cbcrc algorithm by Dick, Josef

“…In this paper we study lattice rules which are cubature formulae to approximate integrands over the unit cube [0,1] s from a weighted reproducing kernel…”
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Lattice rules for nonperiodic smooth integrands by Dick, Josef, Nuyens, Dirk, Pillichshammer, Friedrich

“…The aim of this paper is to show that one can achieve convergence rates of N − α + δ for α > 1 / 2 (and for δ > 0 arbitrarily small) for nonperiodic α -smooth…”
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The weighted star discrepancy of Korobov's p-sets by DICK, JOSEF, PILLICHSHAMMER, FRIEDRICH

“…We prove bounds on the weighted star discrepancy of the p. This implies strong polynomial tractability for the weighted star discrepancy. We also show that a…”
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A simple proof of Stolarsky's invariance principle by BRAUCHART, JOHANN S., DICK, JOSEF

“…-discrepancy and vice versa. In this note we give a simple proof of the invariance principle using reproducing kernel Hilbert spaces.]]>…”
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Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands by Dick, Josef

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DISCREPANCY BOUNDS FOR UNIFORMLY ERGODIC MARKOV CHAIN QUASI-MONTE CARLO by Dick, Josef, Rudolf, Daniel, Zhu, Houying

“…Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can…”
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Construction of interlaced polynomial lattice rules for infinitely differentiable functions by Dick, Josef, Goda, Takashi, Suzuki, Kosuke, Yoshiki, Takehito

“…We study multivariate integration over the s -dimensional unit cube in a weighted space of infinitely differentiable functions. It is known from a recent…”
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Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration by DICK, JOSEF, GOMEZ-PEREZ, DOMINGO, PILLICHSHAMMER, FRIEDRICH, WINTERHOF, ARNE

“…We study high-dimensional numerical integration in the worst-case setting. The subject of tractability is concerned with the dependence of the worst-case…”
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On a projection-corrected component-by-component construction by Dick, Josef, Kritzer, Peter

“…The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several…”
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Exponential convergence and tractability of multivariate integration for Korobov spaces by DICK, Josef, LARCHER, Gerhard, PILLICHSHAMMER, Friedrich, WOZNIAKOWSKI, Henryk

“…In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This…”
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The construction of extensible polynomial lattice rules with small weighted star discrepancy by Dick, Josef

“…In this paper we introduce a construction algorithm for extensible polynomial lattice rules and we prove that the construction algorithm yields generating…”
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Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules by Baldeaux, Jan, Dick, Josef, Leobacher, Gunther, Nuyens, Dirk, Pillichshammer, Friedrich

“…We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate…”
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Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations by Dick, Josef, Kuo, Frances Y., Le Gia, Quoc T., Schwab, Christoph

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Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices by Dick, Josef, Pillichshammer, Friedrich, Suzuki, Kosuke, Ullrich, Mario, Yoshiki, Takehito

“…We prove upper bounds on the order of convergence of lattice-based algorithms for numerical integration in function spaces of dominating mixed smoothness on…”
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On the convergence rate of the component-by-component construction of good lattice rules by Dick, Josef

“…We prove error bounds on the worst-case error for integration in certain Korobov and Sobolev spaces using rank-1 lattice rules with generating vectors…”
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