New Methods for High-Dimensional Verified Quadrature
AbstractConventional verified methods for integration often rely on the verified
bounding of analytically derived remainder formulas for popular
integration rules. We show that using the approach of Taylor models, it
is possible to devise new methods for verified integration of high order
and in many variables. Different from conventional schemes, they do not
require an a-priori derivation of analytical error bounds, but the
rigorous bounds are calculated automatically in parallel to the
computation of the integral.
The performance of various schemes are compared for
examples of up to order ten in up to eight variables. Computational
expenses and tightness of the resulting bounds are compared with
M. Berz, K. Makino, Reliable Computing 5 (1999) 13-22
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