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