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A note on polynomial arithmetic analogue of Halton sequences

Editor: Richard E. Nance Authors:

Shu Tezuka,

Takeshi TokuyamaAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 4, Issue 3

Pages 279 - 284

https://doi.org/10.1145/189443.189447

Published: 01 July 1994 Publication History

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References

[1]

BECK, J., AND CHEN, W. 1987. Irregularities of d~stributlon In Cambrzdge Tracts tn Mathematics. Vol. 89 Cambridge University Press, Cambridge, Mass.

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FAURE, H 1982. Dlscr6pance de suites associ~es a un syst~me de num6ration (en dimensions). Acta Arzthmetzca 41,337-351.

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NIEDERREITER, H. 1992. Random number generation and quasi-Monte Carlo methods, In CBMS-NSF Regional Conference Series zn Applied Math. Vol. 63. Society for Industrial and Applied Math., Philadelphia, Penn.

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TEZUKA, S 1993. Polynomial arithmetic analogue of Halton sequences. ACM Truns. Model. Comput. Szmul. 3, 2, 99 107.

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Niederreiter HXing C(2011)The Algebraic-Geometry Approach to Low-Discrepancy SequencesMonte Carlo and Quasi-Monte Carlo Methods 199610.1007/978-1-4612-1690-2_8(139-160)Online publication date: 23-May-2011
https://doi.org/10.1007/978-1-4612-1690-2_8
Platen E(2008)An introduction to numerical methods for stochastic differential equationsActa Numerica10.1017/S09624929000029208(197)Online publication date: 7-Nov-2008
https://doi.org/10.1017/S0962492900002920
Hartinger JZiegler V(2007)On Corner Avoidance Properties of Random-Start Halton SequencesSIAM Journal on Numerical Analysis10.1137/05064536145:3(1109-1121)Online publication date: 1-May-2007
https://dl.acm.org/doi/10.1137/050645361
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Index Terms

A note on polynomial arithmetic analogue of Halton sequences
1. Computing methodologies
  1. Modeling and simulation
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Numerical differentiation
    2. Quadrature

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A metric result for special sequences related to the Halton sequences

In this paper we investigate a special sequence related to the Halton sequence, namely the Halton sequence indexed by n with R, and prove a metric almost low-discrepancy result.

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cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 4, Issue 3

July 1994

62 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/189443

Editor:
Richard E. Nance
Virginia Tech, Blacksburg, VA

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1994

Published in TOMACS Volume 4, Issue 3

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Niederreiter HXing C(2011)The Algebraic-Geometry Approach to Low-Discrepancy SequencesMonte Carlo and Quasi-Monte Carlo Methods 199610.1007/978-1-4612-1690-2_8(139-160)Online publication date: 23-May-2011
https://doi.org/10.1007/978-1-4612-1690-2_8
Platen E(2008)An introduction to numerical methods for stochastic differential equationsActa Numerica10.1017/S09624929000029208(197)Online publication date: 7-Nov-2008
https://doi.org/10.1017/S0962492900002920
Hartinger JZiegler V(2007)On Corner Avoidance Properties of Random-Start Halton SequencesSIAM Journal on Numerical Analysis10.1137/05064536145:3(1109-1121)Online publication date: 1-May-2007
https://dl.acm.org/doi/10.1137/050645361
Chi HJones E(2007)Research NoteJournal of Parallel and Distributed Computing10.1016/j.jpdc.2007.04.00467:7(876-881)Online publication date: 1-Jul-2007
https://dl.acm.org/doi/10.1016/j.jpdc.2007.04.004
Chi HMascagni M(2007)Efficient Generation of Parallel Quasirandom Faure Sequences Via ScramblingProceedings of the 7th international conference on Computational Science, Part I: ICCS 200710.1007/978-3-540-72584-8_96(723-730)Online publication date: 27-May-2007
https://dl.acm.org/doi/10.1007/978-3-540-72584-8_96
Lemieux C(2006)Chapter 12 Quasi-Random Number TechniquesSimulation10.1016/S0927-0507(06)13012-1(351-379)Online publication date: 2006
https://doi.org/10.1016/S0927-0507(06)13012-1
Schürer RSchmid W(2006)MinT: A Database for Optimal Net ParametersMonte Carlo and Quasi-Monte Carlo Methods 200410.1007/3-540-31186-6_28(457-469)Online publication date: 2006
https://doi.org/10.1007/3-540-31186-6_28
L’Ecuyer PLemieux C(2005)Recent Advances in Randomized Quasi-Monte Carlo MethodsModeling Uncertainty10.1007/0-306-48102-2_20(419-474)Online publication date: 2005
https://doi.org/10.1007/0-306-48102-2_20
Tezuka S(2004)Polynomial Arithmetic Analogue of Hickernell SequencesMonte Carlo and Quasi-Monte Carlo Methods 200210.1007/978-3-642-18743-8_28(451-459)Online publication date: 2004
https://doi.org/10.1007/978-3-642-18743-8_28
Atanassov E(2004)Efficient CPU-Specific Algorithm for Generating the Generalized Faure SequencesLarge-Scale Scientific Computing10.1007/978-3-540-24588-9_12(121-127)Online publication date: 2004
https://doi.org/10.1007/978-3-540-24588-9_12
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Polynomial arithmetic analogue of Halton sequences

Generalized Halton sequences in 2008: A comparative study

A metric result for special sequences related to the Halton sequences

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