On iterated numerical integration

Authors:
Shujun Li;Elise de Doncker;Karlis Kaugars
Affiliations:
Computer Science, Western Michigan University;Computer Science, Western Michigan University;Computer Science, Western Michigan University
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

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Abstract

We revisit the iterated numerical integration method and show that it is extremely efficient in solving certain classes of problems. A multidimensional integral can be approximated by a combination of lower-dimensional or one-dimensional adaptive methods iteratively. When an integrand contains sharp ridges which are not parallel with any axis, iterated methods often outperform adaptive cubature methods in low dimensions. We use examples to support our analysis.