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On the automatic numerical evaluation of definite integrals
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1971
Year
Numerical AnalysisMathematical ProgrammingNumerical ComputationEngineeringLow Precision FormulaeSubdivided RangeMeasurementUncertainty QuantificationCalibrationValidated NumericsDefinite IntegralsInterval AnalysisComputer EngineeringAccuracy And PrecisionInterval ComputationDefinite IntegralApproximation TheoryNumerical Methods
Abstract : A critical examination is made of two common approaches to the automatic evaluation of definite integrals. It is shown that on the grounds of efficiency and reliability it is generally preferable to use families of common point high precision formulae directly over the whole interval of integration than to apply low precision formulae to an adaptively subdivided range. Many examples are given to illustrate the conclusions. (Author)