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Normalization of the Spectral Test in High Dimensions

Author

Listed:
  • Entacher Karl

    (School of Telecommunications Engineering, Salzburg Univ. of Applied Sciences and Technology)

  • Laimer Gerold

    (Department of Scientific Computing, Salzburg University, AUSTRIA)

  • Röck Harald

    (Department of Scientific Computing, Salzburg University, AUSTRIA)

  • Uhl Andreas

    (Department of Scientific Computing, Salzburg University, AUSTRIA)

Abstract

The spectral test provides a reliable measure for lattice assessment and can be computed very efficiently. It has extensively been applied to find good lattices for several MC and QMC applications. In order to enable comparisons across dimensions, a normalized spectral test is widely used. We empirically demonstrate significant shortcomings of this normalization in high dimensions, discuss the empirical distribution of the normalized spectral test values, and propose a new normalization strategy. The new normalization is shown to give more reliable results, especially concerning the comparability of the values accross dimensions.

Suggested Citation

  • Entacher Karl & Laimer Gerold & Röck Harald & Uhl Andreas, 2004. "Normalization of the Spectral Test in High Dimensions," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 265-274, December.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:265-274:n:9
    DOI: 10.1515/mcma.2004.10.3-4.265
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