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Monotonicity of the error term in Gauss-Turán quadratures for analytic function

Published online by Cambridge University Press:  17 February 2009

Gradimir V. Milovanović  and
Miodrag M. Spalević
Gradimir V. Milovanović
Affiliation:
Department of Mathematics, University of Niš, Faculty of Electronic Engineering, P. O. Box 73, 18000 Niš Serbia; e-mail: grade@ni.ac.yu.
Miodrag M. Spalević
Affiliation:
Department of Mathematics and Informatics, University of Kragujevac, Faculty of Science, P. O. Box 60, 34000 Kragujevac, Serbia; e-mail: spale@kg.ac.yu.
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Abstract

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For Gauss–Turán quadrature formulae with an even weight function on the interval [−1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than I, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some ℓ2-error estimates are considered.

Keywords

Gauss–Turán quadratureerror termmonotonicityweight functionanalytic functions
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 4 , April 2007 , pp. 567 - 581
Copyright
Copyright © Australian Mathematical Society 2007

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