Results 91 to 100 of about 3,011 (212)

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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A NOTE ON THE GENERALIZED BERNSTEIN POLYNOMIALS

Honam Mathematical Journal, 2011
Summary: We prove two identities for multivariate Bernstein polynomials on simplices. In this paper, we study good approximations of Bernstein polynomials for every continuous function on simplices and the higher dimensional \(q\)-analogues of Bernstein polynomials on simplices.
Bayad, Abdelmejid, Kim, T., Lee, S.H., Dolgy, D.V.   +3 more
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A resultant matrix for scaled Bernstein polynomials

, 2000
The established theory of the resultant of two polynomials assumes that they are expressed in the power (monomial) basis, and a basis transformation is therefore necessary if the resultant of two Bernstein polynomials is required.
Joab R. Winkler, Winkler, Joab R.
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A note on q-Bernstein polynomials [PDF]

Russian Journal of Mathematical Physics, 2011
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
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Bernstein-type approximations of smooth functions

Statistica, 2007
The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution.
Andrea Pallini
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Bernstein polynomials and bernstein power series

, 1964
PFollowing G.G.Lorentz\u27s book, Bernstein Polynomials, we develop in the first part of this paper the basic properties of the polynomials in the real and complex domains.

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Mixed finite element method with Bernstein elements for the 2D steady Navier-Stokes equations: Stability and implementation

Results in Engineering
This paper introduces a novel mixed finite element method employing Bernstein polynomials to solve the two-dimensional steady Navier-Stokes equations, addressing critical challenges in computational fluid dynamics.
Lanyin Sun, Ziwei Dong
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On Bernstein Polynomials Method to the System of Abel Integral Equations

Abstract and Applied Analysis, 2014
This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the
A. Jafarian, S. Measoomy Nia, Alireza K. Golmankhaneh, D. Baleanu   +3 more
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Flexible Functional Forms Bernstein Polynomials [PDF]

Motivated by the economic theory of cost functions, bivariate Bernstein polynomials are considered for approximating shape-restricted functions that are continuous, non-negative, monotone non-decreasing, concave, and homogeneous of degree one.
Pok Man Chak, Neal Madras, J. Barry Smith   +2 more
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New Operational Matrices of Seventh Degree Orthonormal Bernstein Polynomials

مجلة بغداد للعلوم, 2015
Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)
Baghdad Science Journal
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