ANZIAM  J.  48 (2007), 567-581

Monotonicity of the error term in Gauss–Turán quadratures for analytic functions

Gradimir V. Milovanović   Department of Mathematics   University of Niš   P. O. Box 73   18000 Niš   Serbia     grade@ni.ac.yu Miodrag M. Spalević   Department of Mathematics and Informatics   University of Kragujevac   P. O. Box 60   34000 Kragujevac   Serbia     spale@kg.ac.yu

Abstract

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 1, 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 l^2-error estimates are considered.

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