Abstract. We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x) ≡ w (α,β) we give a necessary and sufficient condition on the parameters α and β such that the optimal averaged Gaussian quadrature formulas are internal.
Abstract. We study the kernels of the remainder term Rn,s(f ) of GaussTurán quadrature formulasfor classes of analytic functions on elliptical contours with foci at ±1, when the weight w is one of the special Jacobi weightsWe investigate the location on the contour where the modulus of the kernel attains its maximum value. Some numerical examples are included.
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