Internality of Two-Measure-Based Generalized Gauss Quadrature Rules for Modified Chebyshev Measures II

Dušan Lj. Djukić, Rada M. Mutavdžić Djukić, Aleksandar V. Pejčev, Lothar Reichel, Miodrag M. Spalević () and Stefan M. Spalević
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Dušan Lj. Djukić: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Rada M. Mutavdžić Djukić: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Aleksandar V. Pejčev: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Lothar Reichel: Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
Miodrag M. Spalević: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Stefan M. Spalević: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: Gaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure d σ ^ . It is important to be able to estimate the quadrature error in the Gaussian rule used. A common approach to estimating this error is to evaluate another quadrature rule that has more nodes and higher algebraic degree of precision than the Gaussian rule, and use the difference between this rule and the Gaussian rule as an estimate for the error in the latter. This paper considers the situation when d σ ^ is a Chebyshev measure that is modified by a linear factor and a linear divisor, and investigates whether the rules in a recently proposed new class of quadrature rules for estimating the error in Gaussian rules are internal, i.e., if all nodes of the new quadrature rules are in the interval ( − 1 , 1 ) . These new rules are defined by two measures, one of which is a modified Chebyshev measure d σ ^ . The other measure is auxiliary.

Keywords: Gauss quadrature rule; averaged Gauss rule; generalized averaged Gauss rule; modified Chebyshev measure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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