Generation of non-uniform low-discrepancy sequences in the multidimensional case

Authors

  • Natalia Roşca “Babes-Bolyai” University, Romania

Keywords:

discrepancy, uniformly distributed sequences, \(G\)-discrepancy, \(G\)-distributed sequences, low-discrepancy sequences, quasi-Monte Carlo integration, interpolation

Abstract

In this paper we extend the results we obtained in an earlier paper, from the one-dimensional case to the \(s\)-dimensional case. We propose two inversion type methods for generating \(G\)-distributed low-discrepancy sequences in \([0,1]^{s}\), where \(G\) is an arbitrary distribution function. Our methods are based on the approximation of the inverses of the marginal distribution functions using linear Lagrange interpolation or cubic Hermite interpolation. We also determine upper bounds for the \(G\)-discrepancy of the sequences we generate using the proposed methods.

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References

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Published

2006-08-01

How to Cite

Roşca, N. (2006). Generation of non-uniform low-discrepancy sequences in the multidimensional case. Rev. Anal. Numér. Théor. Approx., 35(2), 207–219. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2006-vol35-no2-art9

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