ISSN:
0945-3245
Keywords:
AMS(MOS): 65D32
;
CR: G1.4
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary A probabilistic theory for derivation and analysis of error criteria for automatic quadrature is presented. In particular, conditional average error criteria are derived for quadratures which have derivative-bound error estimates. These probabilistic error criteria are compared to variations of heuristic error criteria derived by discretizing the derivative in the original error bound. It is shown that the theory provides a mathematical foundation and a quantitative model for these discrete error criteria. It is also shown that estimating the conditional average error is equivalent to testing error with the spline interpolation as a sample integrand, and that this process can be made implicit by using appropriate error criteria with local error-checks.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01396607
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