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Volume 17,     Number 3,     Fall 2009

 

QUADRATURE ERROR ESTIMATES FOR
INTEGRANDS WITH MODEST
DIFFERENTIABILITY
L. F. SHAMPINE

Abstract. The accuracy of quadrature formulas and their error estimates when the integrand has modest differentiability are studied from several different points of view. The Matlab problem-solving environment (PSE) has three quadrature programs based on formulas of quite different degrees of precision. It is often suggested that formulas of low degree of precision are to be preferred when the integrand is not smooth and not much accuracy is required. Our analysis shows that in this PSE, the formulas of higher degree of precision and their error estimators generally perform at least as well for integrands that are not smooth. They are also more robust because they have better resolution.

 

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