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Mathematics of Computation

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The exact degree of precision of generalized Gauss-Kronrod integration rules


Author: Philip Rabinowitz
Journal: Math. Comp. 35 (1980), 1275-1283
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1980-0583504-6
MathSciNet review: 583504
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Abstract: It is shown that the Kronrod extension to the $n$-point Gauss integration rule, with respect to the weight function $(1 - x^2)^{\mu - 1/2}$, $0 < \mu \leqslant 2$, $\mu \ne 1$, is of exact precision $3n + 1$ for n even and $3n + 2$ for n odd. Similarly, for the $(n + 1)$-point Lobatto rule, with $-1/2< \mu \leqslant 1$, $\mu \ne 0$, the exact precision is $3n$ for $n$ odd and $3n + 1$ for n even.


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Keywords: Kronrod rule, Gauss integration rule, Lobatto integration rule, Gegenbauer polynomials, Szeg&#246; polynomials, Fourier coefficients
Article copyright: © Copyright 1980 American Mathematical Society