Integral and Non-Negativity Preserving Bernstein-Type Polynomial Approximations
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.
International Journal of Computer Mathematics
(2009). Integral and Non-Negativity Preserving Bernstein-Type Polynomial Approximations. International Journal of Computer Mathematics, 86(5), 850-859.
Available at: http://aquila.usm.edu/fac_pubs/1143