数値多重積分に関する話題(<特集>数値計算)

DOI Web Site 被引用文献2件 参考文献13件

書誌事項

タイトル別名
  • On Numerical Multiple Integration(<Special Topics>Numerical Computation)
  • 数値多重積分に関する話題
  • スウチ タジュウ セキブン ニ カンスル ワダイ

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抄録

This paper surveys recent developments on numerical algorithms for high dimensional multiple integration. First, we present Wozniakowski's theorem published in 1991, which revealed a remarkable connection between the integration error and the discrepancy via the classical Wiener measure. Then, we introduce low-discrepancy sequences, by means of which one can compute the arithmetic mean of a number of sample values of the integrand as an approximation to the integration. As a concrete construction method of low-discrepancy sequences, we give the definition of generalized Niederreiter sequences and a brief introduction of Niederreiter-Xing sequences, which are constructed by using algebraic function fields. Finally, we describe Smolyak's algorithm, which is an algorithm computing the weighted mean of sample values of the integrand. Sample points that this algorithm uses are called hyperbolic cross points. An interesting result by Wasilkowski and Wozniakowski on this algorithm is presented.

収録刊行物

  • 応用数理

    応用数理 8 (4), 267-276, 1998

    一般社団法人 日本応用数理学会

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