Geodesic
Comparison of the remainders of the Simpson quadrature formula and the quadrature formula for three-point rational interpolants
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 4, pp. 102-110

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A quadrature formula with positive coefficients is constructed with the use of three nodes $a$, $b$, and $c=(a+b)/2$ and rational interpolants of the form $\rho (x)= \alpha +\beta (x-c)+\gamma/(x-g)$ with a pole $g$ determined by nodes outside the integration interval $[a,b]$. The error of the constructed formula is smaller than the error of the corresponding Simpson quadrature formula if the integrand $f(x)$ has a continuous derivative $f^{(4)}(x)$ on the interval $[a,b]$ and the inequality $f^{(4)}(x) f^{\prime\prime}(x)>0$ is satisfied.
Mots-clés : rational interpolant, quadrature formula
Keywords: Simpson formula. 
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     author = {A.-R. K. Ramazanov and V. G. Magomedova},
     title = {Comparison of the remainders of the {Simpson} quadrature formula and the quadrature formula for three-point rational interpolants},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {102--110},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_4_a7/}
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A.-R. K. Ramazanov; V. G. Magomedova. Comparison of the remainders of the Simpson quadrature formula and the quadrature formula for three-point rational interpolants. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 4, pp. 102-110. http://geodesic.mathdoc.fr/item/TIMM_2021_27_4_a7/