Schur‐convexity and quadrature formulae | Zendy

Franjić Iva | Zendy

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Schur‐convexity and quadrature formulae

Author(s) -

Franjić Iva

Publication year - 2015

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201400227

Subject(s) - mathematics , convexity , monotonic function , quadrature (astronomy) , clenshaw–curtis quadrature , tanh sinh quadrature , gauss–kronrod quadrature formula , gauss–laguerre quadrature , gauss–hermite quadrature , gauss–jacobi quadrature , mathematical analysis , property (philosophy) , gaussian quadrature , nyström method , boundary value problem , financial economics , electrical engineering , economics , engineering , philosophy , epistemology

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).

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