Stieltjes Polynomials and the Error of Gauss-kronrod Quadrature Formulas
نویسنده
چکیده
The Gauss-Kronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the Gauss-Kronrod scheme. An essential progress was made only recently, based on new bounds and as-ymptotic properties for the Stieltjes polynomials. The purpose of this paper is to give a survey on these results. In particular, the quality of the Gauss-Kronrod formula for smooth and for nonsmooth functions is investigated and compared with other quadrature formulas.
منابع مشابه
On Stieltjes Polynomials and Gauss-kronrod Quadrature
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