Results 191 to 200 of about 601,209 (237)

Tensor product q-Bernstein polynomials

BIT Numerical Mathematics, 2008
Given a real number \(q>0\), \(q\)-Bernstein polynomials are a generalization, in the spirit of \(q\)-calculus, of the classical Bernstein polynomials (which can be obtained for \(q=1\)) where some of the integers in the definition of the classical ones are substituted by \(q\)-integers.
Dişibüyük, Çetin, Oruç, Halil
openaire   +2 more sources

A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

Numerical Methods for Partial Differential Equations, 2018
In this paper, we develop an efficient matrix method based on two‐dimensional orthonormal Bernstein polynomials (2D‐OBPs) to provide approximate solution of linear and nonlinear weakly singular partial integro‐differential equations (PIDEs).
Farshid Mirzaee, S. Alipour, Nasrin Samadyar   +2 more
semanticscholar   +1 more source

Consistent approximation of optimal control problems using Bernstein polynomials

IEEE Conference on Decision and Control, 2019
We present a direct method for the solution of nonlinear optimal control problems based on Bernstein polynomial approximations. We show, using a rigorous setting, that the proposed method yields consistent approximations of time continuous optimal ...
V. Cichella, I. Kaminer, Claire Walton, N. Hovakimyan, A. Pascoal   +4 more
semanticscholar   +1 more source

Kantorovich-Bernstein polynomials

Constructive Approximation, 1990
The authors unify the saturation and direct-converse theorems for a steady rate of convergence in \(L_ p[0,1 ...
Ditzian, Zeev, Zhou, Xinlong
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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hertling, Claus, Stahlke, Colin
openaire   +3 more sources

Asymptotics of Differentiated Bernstein Polynomials

Constructive Approximation, 2001
The \(m-\)th derivative of the \(n-\)th order Bernstein polynomial of a function \(f\) is considered for large values of \(n\). For functions \(f\) satisfiyng a certain Lipschitz condition the asymptotics is done by using the Gauss-Weierstrass singular integral.
Impens, C., Vernaeve, H.
openaire   +1 more source

Numerical algorithm for time-fractional Sawada-Kotera equation and Ito equation with Bernstein polynomials

Applied Mathematics and Computation, 2018
The generalized KdV equation arises in many problems in mathematical physics. In this paper, an effective numerical method is proposed to solve two types of time-fractional generalized fifth-order KdV equations, the time-fractional Sawada-Kotera equation
Jiao Wang, T. Xu, Gangwei Wang
semanticscholar   +1 more source

Quantitative generalized Voronovskaja's formulae for Bernstein polynomials

Journal of Approximation Theory, 2018
We give quantitative generalized Voronovskaja’s formulae for Bernstein polynomials which are simple to compute. To achieve this, we obtain explicit and accurate upper estimates for the even central moments of Bernstein polynomials.
J. Adell, D. Cárdenas-Morales
semanticscholar   +1 more source

Evaluating Bernstein–Rabin–Winograd polynomials

Designs, Codes and Cryptography, 2018
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Sebati Ghosh, Palash Sarkar
openaire   +1 more source