New error coefficients for estimating quadrature errors for analytic functions
Authors:
Philip Rabinowitz and Nira Richter
Journal:
Math. Comp. 24 (1970), 561570
MSC:
Primary 65.55
MathSciNet review:
0275675
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Abstract: Since properly normalized Chebyshev polynomials of the first kind satisfy for ellipses with foci at , any function analytic in has an expansion, with . Applying the integration error operator yields . Applying the CauchySchwarz inequality to leads to the inequality . can be computed for any integration rule and approximated quite accurately for Gaussian integration rules. The bound for using this norm is compared to that using a previously studied norm based on Chebyshev polynomials of the second kind and is shown to be superior in practical situations. Other results involving the latter norm are carried over to the new norm.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819700275675X
PII:
S 00255718(1970)0275675X
Keywords:
Error coefficients,
error in numerical integration,
analytic functions,
Chebyshev polynomials,
complete orthonormal set,
error estimates,
trapezoidal rule,
Simpson rule,
norm of error functional,
interpolatory quadrature
Article copyright:
© Copyright 1970
American Mathematical Society
