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The Search for a Good Lattice Augmentation Sequence in Three Dimensions

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Computational Science and Its Applications – ICCSA 2007 (ICCSA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4707))

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Abstract

We describe a systematic approach to the search for a good lattice augmentation sequence in three dimensions, with the index of merit of constituent lattices used as the main criterion of goodness. The result of the search can be used in the construction of an efficient automatic cubature routine for three-dimensional integrals.

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References

  1. Disney, S.A.R., Sloan, I.H.: Lattice integration rules of maximal rank formed by copying rank-1 rules. SIAM Journal on Numerical Analysis 29, 566–577 (1992)

    Article  MATH  Google Scholar 

  2. Hill, M., Robinson, I.: A non-adaptive algorithm for two-dimensional cubature. Journal of Computational and Applied Mathematics 112, 121–145 (1999)

    Article  MATH  Google Scholar 

  3. Li, T., Robinson, I., Hill, M.: The index of merit of kth-copy lattice rules. Journal of Computational and Applied Mathematics (to appear, 2007)

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  4. Robinson, I., Hill, M.: An algorithm for automatic two-dimensional cubature. ACM Transactions on Mathematical Software 28(1), 73–89 (2002)

    Article  Google Scholar 

  5. Sidi, A.: A new variable transformation for numerical integration. International Series of Numerical Mathematics 112, 359–373 (1993)

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  6. Sloan, I.H., Joe, S.: Lattice Methods for Multiple Integration. Oxford University Press, Oxford (1994)

    MATH  Google Scholar 

  7. Wynn, P.: On the convergence and stability of the epsilon algorithm. SIAM Journal on Numerical Analysis 3, 91–122 (1966)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Computer Engineering, La Trobe University, Melbourne, Australia

    Tiancheng Li & Ian Robinson

Authors
  1. Tiancheng Li
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  2. Ian Robinson
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Editor information

Osvaldo Gervasi Marina L. Gavrilova

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© 2007 Springer-Verlag Berlin Heidelberg

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Li, T., Robinson, I. (2007). The Search for a Good Lattice Augmentation Sequence in Three Dimensions. In: Gervasi, O., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2007. ICCSA 2007. Lecture Notes in Computer Science, vol 4707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74484-9_90

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  • DOI: https://doi.org/10.1007/978-3-540-74484-9_90

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74482-5

  • Online ISBN: 978-3-540-74484-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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