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 | References | Similar Articles | Additional Information

Abstract: Filippi [1] has proposed a quadrature scheme for any function in , 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.

**[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)****[2]**C. W. Clenshaw & A. R. Curtis, "A method for numerical integration on an automatic computer,"*Numer. Math.*, v. 2, 1960, pp. 197-205. MR**22**#8659. MR**0117885 (22:8659)****[3]**M. M. Chawla, "On the Chebyshev polynomials of the second kind,"*SIAM Rev.*, v. 9, 1967, pp. 729-733. MR**36**#5583. MR**0222533 (36:5583)****[4]**M. M. Chawla, "Error estimates for the Clenshaw-Curtis quadrature,"*Math. Comp.*, v. 22, 1968, pp. 651-656. MR**37**#3753. MR**0228169 (37:3753)****[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)****[6]**P. J. Davis,*Interpolation and Approximation*, Blaisdell, Waltham, Mass., 1963, pp. 67-68, 311-312. MR**28**#393. MR**0157156 (28:393)**

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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