Bernstein polynomial - Open Access .click

IEEE Transactions on Automatic Control, 2021
In this article, a Bernstein polynomial approach is first applied to the estimation of reachable set for a class of periodic piecewise polynomial systems, whose subsystems are time-varying and can be expanded to Bernstein polynomial forms. A lemma on the
Xiaochen Xie, Chenchen Fan, K. Kwok, J. Lam +3 more
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Fast Funnel Computation Using Multivariate Bernstein Polynomial

IEEE Robotics and Automation Letters, 2021
Guaranteeing safety of robotic systems is essential for a reliable operation. A funnel, the set of states that can be reached from the initial set of states in the presence of disturbances, can be used as a means of safety verification.
Hoseong Seo, C. Son, H. Kim
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Fast Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein Polynomial

, 2021
A new maximum approximate likelihood method for deconvoluting a continuous density on a finite interval in additive measurement error models with known error distribution using the approximate Bernstein polynomial model, a finite mixture of specific beta
Zhong Guan
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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 ...
Lewanowicz, Stanisław, Woźny, Paweł
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