The Bernstein polynomial basis: A centennial retrospective

By Rida T. Farouki. Computer Aided Geometric Design, 2012

563 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/0ad3053eb32ecc5a13d9a6aa868b5c86c5663372

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Citations in the corpus

Most Likely Transformations (2015, methodology): “Recently, transformation models for the direct estimation of conditional distribution functions for arbitrary responses received interest in the context of counterfactual distributions (Chernozhukov et al., 2013), probabilistic forecasting (Gneiting & Katzfuss, 2014), distribution and quantile regre”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, methodology): “For FEA-G, we use elements based on Bernstein polynomials [39,82,100].”
Accurate computations with totally positive Bernstein-Vandermonde matrices (2013, methodology): “The explicit conversion between the Bernstein basis and the power basis is exponentially ill-conditioned as the polynomial degree increases [19, 20], and so it is very important that when designing any algorithm for performing numerical computations with polynomials expressed in Bernstein form, all ”
Bernstein flows for flexible posteriors in variational Bayes (2022, unknown): “Using a BP for approximating g gives the following theoretical guarantees (Farouki 2012) (1) With increasing order M of the BP, the approximation f BP to g gets arbitrarily close (the BP have been introduced for this very purpose in the constructive proof of the Weierstrass theorem by Bernšteın…”
Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013, background): “If the a-th edge (xa,xa+1) is parametrized by t ∈ [0, 1], then φa(t) = (1 − t)(2), φa+n(t) = 2t(1 − t), φa+1(t) = t(2), (31) which are quadratic Bernstein basis functions [48].”
Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount (2019, unknown): “Hence, if G denotes a continuous cdf on [0 , 1] , it can be approximated by the Bernstein estimator of degree m > 0 deﬁned by These so-called Bernstein bases have attractive properties, e.g. , non-negativity, partition of unity and symmetry (see Farouki, 2012, for details).”
Upper Limits on the 21 cm Epoch of Reionization Power Spectrum from One Night with LOFAR (2017, methodology): “We use a Bernstein polynomial of third order as prior on the DD-gain solutions (see e.g. Farouki 2012).”