By D. G. Schweikert
Communications of the ACM,
March 1970,
Vol. 13 No. 3, Pages 163-166
10.1145/362052.362057
Comments
Various simple choices of error improvement estimates for the trapezoid rule are studied to demonstrate a comparison procedure which is relatively independent of the profusion of adaptive search and stopping strategies. Comparisons are based on xr, 0 ≤ r, 0 ≤ x ≤ 1; the inclusion of the non-integer powers makes this more realistic than the usual polynomial based comparison. Behavior near the singularity was found to be the dominant factor, and a new estimate, based on a constant curvature assumption and parametric differences, was considered slightly better than the other choices considered.
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