Calculation of Chakalov-Popoviciu quadratures of Radau and Lobatto type

Abstract

A numerical method for calculation of the generalized Chakalov-Popoviciu quadrature formulae of Radau and Lobatto type, using the results given for the generalized ChakalovPopoviciu quadrature formula, is given. Numerical results are included. As an application we discuss the problem of approximating a function / on the finite interval / = [a, b] by a spline function of degree m and variable defects dv, with n (variable) knots, matching as many of the initial moments of/ as possible. An analytic formula for the coefficients in the generalized Chakalov-Popoviciu quadrature formula is given.