engleski

Schur-convexity and quadrature formulae

This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur-convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur-convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint).

General quadrature formulae; error; Schur-convexity; n-convex functions; Bernoulli polynomials

nije evidentirano