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- W2023505143 abstract "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 use of Gruss, Chebychev and Lupas inequalities, producing a variety of tighter bounds. The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed. The analysis allows the determination of the partition required that would assure that the accuracy the result would be within a prescribed error tolerance. It is demonstrated that the bounds of the approximations are equivalent to those obtained from a Peano kernel that produces Trapezoidal type rules." @default.
- W2023505143 created "2016-06-24" @default.
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- W2023505143 date "2019-06-03" @default.
- W2023505143 modified "2023-09-23" @default.
- W2023505143 title "Midpoint-Type Rules from an Inequalities Point of View" @default.
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- W2023505143 doi "https://doi.org/10.1201/9780429123610-4" @default.
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