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.

adaptive integration, error improvement estimate,
trapezoid rule, nonpolynomial error criteria

5.16

CA700305 JB February 13, 1978  4:47 PM

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