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Error estimates for a Chebyshev quadrature method


Author: N. K. Basu
Journal: Math. Comp. 24 (1970), 863-867
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1970-0277111-6
MathSciNet review: 0277111
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Abstract: Filippi [1] has proposed a quadrature scheme for any function $ f(x)$ in $ [ - 1,1]$, based on expanding the integrand in a series of Chebyshev polynomials of the second kind. In this paper the error associated with this quadrature method when applied to analytic functions has been investigated in detail.


References [Enhancements On Off] (What's this?)

  • [1] S. Filippi, "Angenäherte Tschebyscheff-Approximation einer Stammfunktion--eine Modifikation des Verfahrens von Clenshaw und Curtis," Numer. Math., v. 6, 1964, pp. 320-328. MR 30 #710. MR 0174914 (30:5105)
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  • [5] M. M. Chawla & M. K. Jain, "Error estimates for Gauss quadrature formulas for analytic functions," Math. Comp., v. 22, 1968, pp. 82-90. MR 36 #6142. MR 0223093 (36:6142)
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0277111-6
Keywords: Chebyshev quadrature method, function of bounded variation, expansion, Chebyshev polynomials of second kind, Lagrange interpolation polynomial, analytic functions, contour integral estimate of error
Article copyright: © Copyright 1970 American Mathematical Society

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