Papers by Peter Hellekalek
arXiv (Cornell University), May 9, 2016
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Acta Arithmetica, 2012
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Acta Arithmetica, 1994
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Acta Arithmetica, 1997
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ABSTRACT
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ABSTRACT
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ACM SIGSIM Simulation Digest, 1998
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Springer Proceedings in Mathematics & Statistics, 2012
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Proceedings of the 27th conference on Winter simulation - WSC '95, 1995
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Lecture Notes in Statistics, 1998
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Lecture Notes in Statistics, 1998
The Monte Carlo and the quasi-Monte Carlo method are two of the most important techniques to solv... more The Monte Carlo and the quasi-Monte Carlo method are two of the most important techniques to solve multidimensional problems. In both cases, we employ deterministic algorithms to generate finite point sets in high dimensions. The quality of the equidistribution of these point sets may have a decisive influence on our numerical results. In this contribution, we will discuss the main concepts to assess equidistribution. In particular, we will present a new interpretation of the well-known spectral test.
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Random and Quasi-Random Point Sets, 1998
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Monte-Carlo and Quasi-Monte Carlo Methods 1998, 2000
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Theoretical Computer Science, 1989
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Monatshefte f�r Mathematik, 1995
The classical Erdös-Turán-Koksma inequality gives us an upper bound for the discrepancy of a sequ... more The classical Erdös-Turán-Koksma inequality gives us an upper bound for the discrepancy of a sequence in thes-dimensional unit cube in terms of exponential sums, more precisely, in terms of the trigonometric function system.
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Monatshefte für Mathematik, 2013
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Monatshefte f�r Mathematik, 1979
ABSTRACT
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Monatshefte f�r Mathematik, 1992
Leta be irrational and letf:[0,1]?R be Riemann-integrable with integral zero. Letfn(x) denote the... more Leta be irrational and letf:[0,1]?R be Riemann-integrable with integral zero. Letfn(x) denote the Weyl sumfn(x):=?k=0n-1f({xka>}),x?R/Z?[0,1[,n?N. We prove criteria for the boundedness of the sequence (fn)n=1 and discuss the relation of this question to irregularities of the distribution of sequences.
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Papers by Peter Hellekalek