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Generalized Chebyshev interpolation and its application to automatic quadrature


Authors: Takemitsu Hasegawa, Tatsuo Torii and Ichizo Ninomiya
Journal: Math. Comp. 41 (1983), 537-553
MSC: Primary 65D32; Secondary 41A55, 65D05
DOI: https://doi.org/10.1090/S0025-5718-1983-0717701-6
Corrigendum: Math. Comp. 47 (1986), 385.
MathSciNet review: 717701
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Abstract: A generalized Chebyshev interpolation procedure increasing a fixed number of sample points at a time is developed and analyzed. It is incorporated into an efficient automatic quadrature scheme of Clenshaw-Curtis type. Numerical examples indicate that the present method is efficient not only for well-behaved functions but for those with discontinuous low order derivatives by virtue of adequate error estimation as well as saving of sample points.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0717701-6
Keywords: Chebyshev interpolation, approximate integration, Clenshaw-Curtis scheme, automatic quadrature
Article copyright: © Copyright 1983 American Mathematical Society