Inequalities of Ostrowski-Grüss type and applications
Some new inequalities of Ostrowski-Grüss type are derived. They are applied to the error analysis for some Gaussian and Gaussian-like quadrature formulas.
Some new inequalities of Ostrowski-Grüss type are derived. They are applied to the error analysis for some Gaussian and Gaussian-like quadrature formulas.
We discuss recent results on constructing approximating schemes based on averaged values of the approximated function f over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of f over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.
Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics. We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds to enable software...