Generalized Chebyshev interpolation and its application to automatic quadrature

A generalized Chebyshev interpolation procedure increasing a fixed number of sample points at a time is developed and analvzed. It is incorporated into an efficient automatic quadrature scheme of Clenshaw-Curtis tvpe. Numerical examples indicate that the present method is efficient not onlv for well-behaved functions but for those w^ith discontinuous low order derivatives by virtue of adequate error estimation as wvell as saving of sample points.