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 1352 4 2093 1352 4 2093 1352 4 2093 1352 4 2093 2048 4 2093 2048 4 2093 2074 4 2093 2074 4 2093 2074 4 2093 2093 4 2093 2093 4 2093 2093 4 2093 2093 4 2093 2093 4 2093 2093 4 2093 2550 4 2093 2550 4 2093 1092 5 2093 1298 5 2093 1573 5 2093 2093 5 2093 2093 5 2093 2093 5 2093 429 5 2093 834 5 2093 872 5 2093