Integral and Non-Negativity Preserving Bernstein-Type Polynomial Approximations

Document Type

Article

Publication Date

2009

Department

Mathematics

School

Mathematics and Natural Sciences

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.

Publication Title

International Journal of Computer Mathematics

Volume

86

Issue

5

First Page

850

Last Page

859

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