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Multiple integration is intractable but not hopeless

Published online by Cambridge University Press:  17 February 2009

Ian H. Sloan
Ian H. Sloan
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia.
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Multiple integrals in ten or twenty variables are often needed by atomic, molecular and nuclear physicists, because of the large number of degrees of freedom in the quantum systems with which they must deal. In statistics too there is often a need to evaluate integrals with many degrees of freedom. It is in mathematical finance, however, that the most striking examples are seen, with claims of integrals being evaluated during recent years with many hundreds of variables.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 3 - 8
Copyright
Copyright © Australian Mathematical Society 2000

References

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[4]Sloan, I. H. and Joe, S., Lattice Methods for Multiple Integration (Oxford University Press, 1994).CrossRefGoogle Scholar
[5]Sloan, I. H. and Wozniakowski, H., “An intractability result for multiple integration”, Mathematics of Computation 66 (1997) 1119–1124.CrossRefGoogle Scholar