The Exact Degree of Precision of Generalized Gauss-Kronrod Integration Rules
نویسندگان
چکیده
It is shown that the Kronrod extension to the «-point Gauss integration rule, with respect to the weight function (1 x2)V~"2, 0 < M < 2, ju i= 1, is of exact precision 3n + 1 for n even and 3n + 2 for n odd. Similarly, for the (n-t-l)-point Lobatto rule, with — V¡ < M < 1, u ^ 0, the exact precision is 3n for n odd and 3n + 1 for n even.
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Department of Mathematics, University of Gaziantep, Gaziantep, Turkey e-mail address : [email protected] Abstract For the practical estimation of the error of Gauss quadrature rules Gauss-Kronrod rules are widely used; but, it is well known that for the generalized Hermite weight function, ωα(x) = |x|2α exp(−x2) over [−∞,∞], real positive Gauss-Kronrod rules do not exist. Among the alternati...
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