Summary
In this paper we investigate quadrature formulas over a finite intervall [a, b] whose remainder may be represented asR(f)=c kn f (2k)(ξ), where ξ∈(a, b), c kn is a positive or negative constant for allf∈C 2k[a, b] andn+1 denotes the number of nodes. We determine thek andn, for which there will exist optimal formulas of this type. When the nodes are equidistant we establish inclusions for the optimalc kn and construct simple formulas with the same type of remainder which attain asymptotically for largen the precision of the optimal ones.
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Schmeißer, G. Optimale Quadraturformeln mit semidefiniten Kernen. Numer. Math. 20, 32–53 (1972). https://doi.org/10.1007/BF01436641
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DOI: https://doi.org/10.1007/BF01436641