A Comparison of Error Improvement Estimates
for Adaptive Trapezoid Integration
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 x^r, `; the inclusion
of the noninteger 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.
CACM March, 1970
Schweikert, D. G.
