Results 81 to 90 of about 43,913 (238)

Bernstein polynomials and learning theory

Journal of Approximation Theory, 2004
Let \(f(x)= -x\log x- (I- x)\log(1 - x)\) for \(0\leq x\leq 1\); it is referred to as the entropy function. Let \(B_n[f]\) denote the nth Bernstein polynomial of \(f\). One half of the paper establishes the estimates \[ f(x)- B_n[f](x)\geq {1\over 2n}+ {1\over 20n^2 x(1-x)}- {1\over 12n^2}\text{ for }{15\over n}\leq x\leq 1-{15\over n}, \] \[ \lim_{n ...
Dietrich Braess, Tomas Sauer
openaire   +2 more sources

Approximation of Discontinuous Functions by Positive Linear Operators. A Probabilistic Approach

Mathematical Methods in the Applied Sciences, Volume 49, Issue 5, Page 4184-4197, 30 March 2026.
ABSTRACT We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms of a local first modulus of continuity, are best possible, in the sense that we can construct particular ...
J.A. Adell, P. Garrancho, F.J. Martínez‐Sánchez   +2 more
wiley   +1 more source

Efficient discontinuous Galerkin finite element methods via Bernstein polynomials [PDF]

, 2015
Robert C. Kirby
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Area of Bernstein-Type Polynomials [PDF]

Proceedings of the American Mathematical Society, 1974
Bernstein polynomials in one variable are known to be total-variation diminishing when compared to the approximated function f. Here we consider the two variable case and give a counterexample to show they are not area-diminishing. Sufficient conditions are then given on a continuous function f to insure convergence in area. A similar theorem is proved
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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  

Consistency of Bernstein Polynomial Posteriors

Journal of the Royal Statistical Society Series B: Statistical Methodology, 2002
SummaryA Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose densities are mixtures of known beta densities. The Bernstein prior is of interest in Bayesian nonparametric inference with continuous data.
PETRONE, SONIA, WASSERMAN L.
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Constrained Path Planning for Soft Continuum Robots With Bernstein Surfaces

IEEE Open Journal of Control Systems
This manuscript presents a framework for trajectory generation for soft continuum robots using principles from optimal control. The problem is constrained over the partial differential kinematic equations of the Cosserat rod model, capturing all modes of
Maxwell Hammond, Ean Lovett, Vincenzo Pugliese, Venanzio Cichella, Caterina Lamuta   +4 more
doaj   +1 more source

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).
openaire   +1 more source

Uniform And Pointwise Polynomial Inequalities In Regions With Asymptotically Conformal Curve

MANAS: Journal of Engineering, 2018
In this we continue studying the Nikolskii and Bernstein-Walsh type polynomial estimation in the Lebesgue spaces in the bounded and unbounded regions bounded by asymptotically conformal ...
P. Özkartepe
doaj  

A new approach for solving Bratu’s problem

Demonstratio Mathematica, 2019
A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique.
Ghomanjani Fateme, Shateyi Stanford
doaj   +1 more source