New Error Coefficients for Estimating Quadrature Errors for Analytic Functions
نویسندگان
چکیده
منابع مشابه
New Error Coefficients for Estimating Quadrature Errors for Analytic Functions
Since properly normalized Chebyshev polynomials of the first kind T„(z) satisfy (?„, ?„) = [ f,(z)7ÜÖ |1 z2\~TM\dz\ = Smn for ellipses ep with foci at ± 1, any function analytic in ep has an expansion,/(z) = J3 anfn{z) with a„ = (/, Tn). Applying the integration error operator E yields E(J) = 2~Z a„E(Tn)Applying the Cauchy-Schwarz inequality to E(J) leads to the inequality |£CDIsá Z W¿2\E(Tn)\2...
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1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...
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In the Hestenes-Stiefel method, the corresponding count is 2ra2 + 5ra + 4. In the latter method, if p„ in the last step were to be computed from the recursion relation, the method would win back the n2 multiplications which it lost to the Craig method in the first step ; but it would hardly be reasonable to calculate the last residual in this way. We note that since the algorithm in either case...
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In the Hestenes-Stiefel method, the corresponding count is 2ra2 + 5ra + 4. In the latter method, if p„ in the last step were to be computed from the recursion relation, the method would win back the n2 multiplications which it lost to the Craig method in the first step ; but it would hardly be reasonable to calculate the last residual in this way. We note that since the algorithm in either case...
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We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1970
ISSN: 0025-5718
DOI: 10.2307/2004831