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Degenerate Bernstein polynomials [PDF]

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2018
9
Taekyun Kim, Dae San Kim, Kim Dae San
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Generalized Bernstein Polynomials

BIT Numerical Mathematics, 2004
The authors define generalized Bernstein polynomials of degree \(n\), for \(n \in \mathbb{N}\) and \(i \in \{0,1,\dots,n\}\), by \[ B_i^n(x;\omega| q):= \frac{1}{(\omega;q)_n} \begin{bmatrix} n \\i \end{bmatrix}_q x^i(\omega x^{-1};q)_i(x;q)_{n-i}. \] Here \(q\) and \(\omega\) are real parameters such that \(q \neq 1\) and \(\omega \neq 1,q^{-1},\dots ...
Stanisław Lewanowicz, Paweł Wozny
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Random Bernstein Polynomials

Scandinavian Journal of Statistics, 1999
Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a ...
Sonia Petrone
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On Generalized Bernstein Polynomials

SIAM Journal on Mathematical Analysis, 1974
The generalized Bernstein polynomials of Jakimovski and Leviatan and the generalized Euler summability method of Wood are considered in the general context of Gronwall-like transformations. It is shown under general circumstances that, for bounded sequences, generalized Euler summability is equivalent to Euler summability.
Bustoz, J., Groetsch, C. W.
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An identity for multivariate Bernstein polynomials

Computer Aided Geometric Design, 2003
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Kurt Jetter, Joachim Stöckler
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Approximation by Bernstein Polynomials

American Journal of Mathematics, 1994
Let \[ B_ n(f; x)= \sum^ n_{k=0} f\left({k\over n}\right)\left(\begin{smallmatrix} n\\ k\end{smallmatrix}\right) x^ k(1-x)^{n- k} \] and \(w_ \varphi(f; \delta)= \sup_{0\leq t\leq \delta} \sup_ x| f(x- t\varphi(x))- 2f(x)+ f(x+ t\varphi(x)))|\), where \(f\in C[0,1]\), \(\varphi(x)= \sqrt{x(1-x)}\) and the second supremum is taken for those values of ...
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Bernstein Polynomial and Tjurina Number

Geometriae Dedicata, 1999
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Hertling, Claus, Stahlke, Colin
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Multivariate Bernstein polynomials and convexity

Computer Aided Geometric Design, 1991
Many properties of a univariate convex function are known to be associated with those of the Bernstein polynomials of the same function. Yet, this often doesn't hold for multivariate functions. The author presents two new conceptions of convexity. One of them is the axial convexity, which is close to the classical definition and suggests a function's ...
Thomas Sauer
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Moment Sequences and the Bernstein Polynomials*

Canadian Mathematical Bulletin, 1969
The Bernstein polynomials(1.1)and the Bernstein power series(1.2)have been the subject of much research (e. g. [1; 2; 3; 6; 7; 8]). It is the purpose of this paper to demonstrate the relationship between these linear operators and certain classes of moment sequences defined below.
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On simulating a class of Bernstein polynomials

ACM Transactions on Modeling and Computer Simulation, 2012
Given a black box that generates independent Bernoulli samples with an unknown bias p, we consider the problem of simulating a Bernoulli random variable with bias f ( p ) (where f is a given function) using a finite (computable in advance) number of independent ...
Vineet Goyal, Karl Sigman
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