Positivity of the weights of extended Clenshaw-Curtis quadrature rules

Hasegawa, Takemitsu; Sugiura, Hirosi; Torii, Tatsuo

doi:10.1090/S0025-5718-1993-1176710-2

Positivity of the weights of extended Clenshaw-Curtis quadrature rules
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by Takemitsu Hasegawa, Hirosi Sugiura and Tatsuo Torii PDF

Math. Comp. 60 (1993), 719-734 Request permission

Abstract:

We prove that some extended Clenshaw-Curtis quadrature rules have all weights positive. We also present extended Filippi rules of open type having all weights positive. Conjectures on the possibility of other positive quadrature rules embedded in Clenshaw-Curtis or Filippi rule are suggested.

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Algorithm 655-IQPACK: FORTRAN subroutines for the weights of interpolatory quadratures

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