An Extremal Approach to Birkhoff Quadrature Formulas (Journal of Computational Mathematics, 2001)
As we know, a solution of an extremal problem with Hermite interpolation constraints is a system of nodes of corresponding Gaussian Hermite quadrature formula (the so-called Jacobi approach). But this conclusion is violated for a Birkhoff quadrature formula. In this paper an extremal problem with Birkhoff interpolation constraints is discussed, from which a large class of Birkhoff quadrature formulas may be derived.
Keywords: An extremal approach; Birkhoff quadrature formulas.