Error estimates for Gauss–Turán quadratures and their Kronrod extensions
نویسندگان
چکیده
We study the kernel Kn,s(z) of the remainder term Rn,s( f ) of Gauss–Turán–Kronrod quadrature rules with respect to one of the generalized Chebyshev weight functions for analytic functions. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L∞-error bounds of Gauss–Turán–Kronrod quadratures. Following Kronrod, using the modulus of the difference of Gauss–Turán quadratures and their Kronrod extensions, we derive new error estimates for Gauss–Turán quadratures and compare them with the effective L1-error bounds derived in Milovanović & Spalević (2005, BIT, 45, 117–136).
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