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Handbook of Analytic Computational Methods in Applied Mathematics
The article investigates interior point rules which contain the midpoint as a special case, and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. Thus the simplest open Newton-Cotes rules are examined. Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms. Perturbed quadrature rules are obtained through the usedoi:10.1201/9781420036053.ch4 fatcat:smsoxua2h5bmxn527ivn23kf34