Acu, Ana Maria; Rafiq, Arif; Sofonea, Florin Some new four-point quadrature formulas. (English) Zbl 1199.65073 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 17, No. 3, 1-13 (2009). Summary: We present a new family of four-point quadrature formulas of close type. These quadrature formulas can be considered as generalizations of Gauss, Newton, Simpson and Lobatto quadrature formulas for different classes of functions. The optimal quadrature formulas in the sense of minimal errors are obtained. An analysis of error inequalities for different classes of functions is also given. MSC: 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures Keywords:quadrature rule; error inequalities; generalizations of Gauss, Newton, Simpson and Lobatto quadrature formulas PDFBibTeX XMLCite \textit{A. M. Acu} et al., An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 17, No. 3, 1--13 (2009; Zbl 1199.65073) Full Text: EuDML