Lagrange and Least-Squares Polynomials as Limits of Linear Combinations of Iterates of Bernstein and Durrmeyer Polynomials Original Research Article

The linear combination of iterates 1−(1 − Pn)M of Bernstein and Durrmeyer operators of a fixed degree n is considered for increasing order of iteration M. The resulting sequence of polynomials is shown to converge to the Lagrange interpolating polynomial for the Bernstein operators, and the least-squares approximating polynomial for the Durrmeyer operators.