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Positivity of the weights of extended Clenshaw-Curtis quadrature rules. (English) Zbl 0779.65014

Extended Clenshaw-Curtis quadrature rules are defined by adding abscissae which are chosen as the zeros of certain polynomials such that embedded sequences of nodes are created. In a similar way, Filippi rules of open type are treated.
The authors prove two main theorems showings that these quadrature rules have all weights positive. Some conjectures on the possibility of other positive quadrature rules are submitted at the end of the paper.

MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
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