Integral and non-negativity preserving Bernstein-type polynomial approximations

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International Journal of Computer Mathematics, ISSN: 0020-7160, Vol: 86, Issue: 5, Page: 850-859

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Ding, Jiu; Kolibal, Joseph; Rhee, Noah H.
Informa UK Limited
Mathematics; Computer Science; integral preserving; positivity preserving; bernstein-type polynomials; Physical Sciences and Mathematics
article description
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. © 2009 Taylor & Francis.