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Mathematics of Computation

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On the definiteness of Gauss-Kronrod integration rules

Author: Philip Rabinowitz
Journal: Math. Comp. 46 (1986), 225-227
MSC: Primary 65D30
MathSciNet review: 815844
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Abstract: The nondefiniteness of the Kronrod extension of the Gauss-Gegenbauer integration rule with weight function $w(x;\mu ) = {(1 - {x^2})^{\mu - 1/2}}$, $0 < \mu < 1$, is shown when there are more than three abscissas.

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Keywords: Definite integration rule, Kronrod rule, Gauss integration rule, Gegenbauer polynomials, Szeg&#246; polynomials
Article copyright: © Copyright 1986 American Mathematical Society