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Error estimates for Gaussian quadratures of analytic functions

✍ Scribed by Gradimir V. Milovanović; Miodrag M. Spalević; Miroslav S. Pranić

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
417 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes > 1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.

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