Generalized Clenshaw-Curtis quadrature rule with application to a collocation least-squares method (Q2383813)

The authors establish a quadrature formula on convex domains by using scattered abscissas. This formula may be viewed as an extension of the Clenshaw-Curtis rule. A convergence analysis is established for a collocation least-square scheme using scattered abscissas as collocation points in the sense of a Legendre weighted Sobolev norm. Numerical experiments are provided in the case of a linear system.