05038966

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05038966 Guessab, Allal On a new family of Gaussian quadrature formulae of Birkhoff type with applications to polynomial inequalities. J. Concr. Appl. Math. 3, No. 2, 127-168 (2005). 2005 Eudoxus Press, LLC, Cordova, TN EN quasi-orthogonal polynomials symmetric tridiagonal matrix Zbl 0479.65001 A certain type of Gauss quadrature formulae with derivatives in the interior points of the integration interval is considered. The author discusses the possibility to construct these quadrature formulae by means of eigenvalues and eigenvectors of a symmetric three-diagonal matrix. At the same time he presents numerical comparisons with the classical Gaussian quadrature formulae. Some inequalities are obtained as direct applications of the new quadrature formulae. About the efficiency of the said quadrature formulae see {\it W. Gautschi} [A survey of Gauss-Christoffel quadrature formulae, in E. B. Christoffel: the influence of his work on mathematics and the physical sciences, Int. Symp., Aachen 1979, 72--147 (1981; Zbl 0479.65001)]. Vladimir N. Karpushkin (Moskva)