Integral and non-negativity preserving Bernstein-type polynomial approximations

Abstract

In this paper, we consider the problem of approximating a function by Bernstein-type polynomials that preserve the integral and non-negativity of the original function on the interval [0, 1], obtaining the Kantorovich–Bernstein polynomials, but providing a novel approach with advantages in numerical analysis. We then develop a Markov finite approximation method based on piecewise Bernstein-type polynomials for the computation of stationary densities of Markov operators, providing numerical results for piecewise constant and piecewise linear algorithms.

Keywords:

• integral preserving
• positivity preserving
• Bernstein-type polynomials

AMS Subject Classifications :

• 41A10
• 41A35
• 65J10