Titlebook: Numerical Integration; Proceedings of the C G. H?mmerlin Conference proceedings 1982 Springer Basel AG 1982

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Optimal Quadrature of Convex Functions,At the instigation of H. Brass we consider the following question: Let us assume that for given fixed nodes a=x.

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Gaussian Cubature Formulae of Degree 2 and 3,For integrals with convex domains of integration we consider cubature formulae of degree r, r∈{2, 3}, with only positive weights and all nodes inside the domain. We show, that the minimal number of nodes for such formulae varies from 3 to at least 5 (for r=2) and from 3 to at least 9 (for r=3) in dependence of the shape of the domain.

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Gaussian Quadrature Applied to Eigenvalue Approximations,We consider the eigenvalue problem . , with K : X → X, X = L. (I), a compact integral operator. In order to obtain approximations x. resp. y. for elements of . resp.

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