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A Comparison of Subdivision Strategies for Verified Multi-Dimensional Gaussian Quadrature

In: Developments in Reliable Computing

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  • Bruno Lang

    (Aachen University of Technology, Computing Center)

Abstract

This paper compares several strategies for subdividing the domain in verified multidimensional Gaussian quadrature. Subdivision may be used in two places in the quadrature algorithm. First, subdividing the box can reduce the over-estimation of the partial derivatives’ ranges, which are needed to bound the approximation error. Second, if the required error bound cannot be met with the whole domain then the box is split into subboxes, and the quadrature algorithm is recursively applied to these. Both variants of subdivision are considered in this paper.

Suggested Citation

  • Bruno Lang, 1999. "A Comparison of Subdivision Strategies for Verified Multi-Dimensional Gaussian Quadrature," Springer Books, in: Tibor Csendes (ed.), Developments in Reliable Computing, pages 67-75, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-1247-7_6
    DOI: 10.1007/978-94-017-1247-7_6
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