Convergence of Generalized Bernstein Polynomials
نویسندگان
چکیده
منابع مشابه
Some new properties of Generalized Bernstein polynomials
Let Bm(f) be the Bernstein polynomial of degree m. The Generalized Bernstein polynomials
متن کاملGeneralized Bernstein Polynomials and Symmetric Functions
We begin by classifying all solutions of two natural recurrences that Bernstein polynomials satisfy. The first scheme gives a natural characterization of Stancu polynomials. In Section 2, we identify the Bernstein polynomials as coefficients in the generating function for the elementary symmetric functions, which gives a new proof of total positivity for Bernstein polynomials, by identifying th...
متن کاملOn the Convergence and Iterates of q-Bernstein Polynomials
The convergence properties of q-Bernstein polynomials are investigated. When q > 1 is fixed the generalized Bernstein polynomials Bnf of f , a one parameter family of Bernstein polynomials, converge to f as n → ∞ if f is a polynomial. It is proved that, if the parameter 0 < q < 1 is fixed, then Bnf → f if and only if f is linear. The iterates of Bnf are also considered. It is shown that B n f c...
متن کاملConvergence Rates for Density Estimation with Bernstein Polynomials
Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior i...
متن کاملConvergence of rational Bernstein operators
In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Piţul and P. Sablonnière. It is shown that the rational Bernstein operators converge to the identity operator if and only if the maximal difference between two consecutive nodes is converging to zero. Further a Voronovskaja theorem is given based on the explicit computation of hi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2002
ISSN: 0021-9045
DOI: 10.1006/jath.2001.3657