Results 111 to 120 of about 601,209 (237)

q-Bernstein polynomials and Bézier curves

Journal of Computational and Applied Mathematics, 2003
Bézier curve techniques are extended by using a generalization of the Bernstein basis, called the \(q\)-Bernstein basis. A one-parameter family of generalized Bernstein polynomial is defined. It is proved that the approximation to a convex function by its \(q\)-Bernstein polynomials is one sided. It is shown also that the difference of two consecutive \
Oruc, Halil, Phillips, Gm
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Direct Estimate for Bernstein Polynomials

Journal of Approximation Theory, 1994
The following pointwise approximation for the Bernstein polynomials \(B_ n (f,x)= \sum_{k=0}^ n {\binom nk} x^ k (1-x)^{n -k} f(k/n)\) are proved: \[ | B_ n (f,x)- f(x)|\leq C\omega^ 2_{\varphi^ \lambda} (f, n^{-1/2} \varphi (x)^{1- \lambda}), \qquad 0\leq \lambda\leq 1, \quad \varphi(x)^ 2= x(1-x).
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Some Identities on the Twisted (ℎ,𝑞)-Genocchi Numbers and Polynomials Associated with 𝑞-Bernstein Polynomials

International Journal of Mathematics and Mathematical Sciences, 2011
We give some interesting identities on the twisted (ℎ,𝑞)-Genocchi numbers and polynomials associated with 𝑞-Bernstein polynomials.
Seog-Hoon Rim, Sun-Jung Lee
doaj   +1 more source

A semi-parametric model for circular data based on mixtures of beta distributions [PDF]

This paper introduces a new, semi-parametric model for circular data, based on mixtures of shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial density model which is well known to provide good approximations to
Jose Antonio Carnicero, Michael P. Wiper
core  

Bernstein computational algorithm for integro-differential equations

Partial Differential Equations in Applied Mathematics
In this study, we introduce a computational algorithm for solving Integro-Differential Equations (IDEs) using Bernstein polynomials as basis functions.
Taiye Oyedepo, Ganiyu Ajileye, Abayomi Ayotunde Ayoade   +2 more
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A Study on the -Adic Integral Representation on Associated with Bernstein and Bernoulli Polynomials

Advances in Difference Equations, 2010
We consider the Bernstein polynomials on and investigate some interesting properties of Bernstein polynomials related to Stirling numbers and Bernoulli numbers.
Kim Won-Joo, Simsek Yilmaz, Jang Lee-Chae   +2 more
doaj  

Circular Bernstein polynomial distributions [PDF]

This paper introduces a new non-parametric approach to the modeling of circular data, based on the use of Bernstein polynomial densities which generalizes the standard Bernstein polynomial model to account for the specific characteristics of circular ...
Concepción Ausín, José Antonio Carnicero, Michael P. Wiper   +2 more
core  

Numerical Solution of Time-Fractional Order Telegraph Equation by Bernstein Polynomials Operational Matrices

, 2016
We present a new method to solve time-fractional order telegraph equation (TFOTE) by using Bernstein polynomials. By implementation of Bernstein polynomials operational matrices of fractional differential on TFOTE, we reduce the original problem to a ...
M. Asgari, R. Ezzati, T. Allahviranloo
semanticscholar   +1 more source

Iterates of Bernstein polynomials [PDF]

Pacific Journal of Mathematics, 1967
Kelisky, R. P., Rivlin, T. J.
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Faster approximation to multivariate functions by combined Bernstein-Taylor operators

Demonstratio Mathematica
In this article, we incorporate multivariate Taylor polynomials into the definition of the Bernstein operators to get a faster approximation to multivariate functions by these combined operators.
Duman Oktay
doaj   +1 more source