The Trigonometric Polynomial Like Bernstein Polynomial [PDF]
The Scientific World Journal, 2014 A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed.
Xuli Han
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Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems [PDF]
Sensors, 2022 This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear ...
Calvin Kielas-Jensen +5 more
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Semi-Parametric Estimation Using Bernstein Polynomial and a Finite Gaussian Mixture Model [PDF]
Entropy, 2022 The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact ...
Salima Helali +2 more
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On nonparametric estimating ROC curve based on non-uniform rational B-spline. [PDF]
PLoS ONEThe receiver operating characteristic (ROC) curve is a commonly used statistical method to assess the efficacy of a diagnostic test or biomarker measured on a continuous scale. This work presents a versatile approach using a non-uniform rational B-spline
Mahmut Sami Erdoğan
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Improved Multiscale Structural Mapping with Supervertex Vision Transformer for the Detection of Alzheimer's Disease Neurodegeneration. [PDF]
Hum Brain MappWe propose MSSM+, an extension of multiscale structural mapping (MSSM), together with surface supervertex mapping (SSVM) and a Supervertex Vision Transformer (SV‐ViT). Together, these methods exhibited better performance in detecting Alzheimer's disease and less variability across MR vendors than MSSM.
Baek G +3 more
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The Stability Analysis of Linear Systems with Cauchy—Polynomial-Vandermonde Matrices
Axioms, 2023 The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein–Vandermonde matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi ...
Mutti-Ur Rehman +3 more
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Consistency of Approximation of Bernstein Polynomial-Based Direct Methods for Optimal Control
Machines, 2022 Bernstein polynomial approximation of continuous function has a slower rate of convergence compared to other approximation methods. “The fact seems to have precluded any numerical application of Bernstein polynomials from having been made.
Venanzio Cichella +4 more
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On Bernstein’s inequality for polynomials [PDF]
Analysis and Mathematical Physics, 2019 Bernstein's classical inequality asserts that given a trigonometric polynomial $T$ of degree $n\geq1$, the sup-norm of the derivative of $T$ does not exceed $n$ times the sup-norm of $T$. We present various approaches to prove this inequality and some of its natural extensions/variants, especially when it comes to replacing the sup-norm with the $L^p ...
Queffélec, Hervé, Zarouf, Rachid
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Use of Bernstein Polynomial in Numerical Solution of Nonlinear Fred Holm Integral Equation [PDF]
Engineering and Technology Journal, 2011 In this paper, Bernstein polynomials with different degree has been used to approximate the solution of nonlinear Fredholm integral equations. A comparison between the different degree of Bernstein polynomials has been made depending on absolute error ...
Khawla A .AL-Zubaidy, Muna M. Mustafa
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface
Journal of Mathematics, 2022 A computational model is presented to find the q-Bernstein quasi-minimal Bézier surfaces as the extremal of Dirichlet functional, and the Bézier surfaces are used quite frequently in the literature of computer science for computer graphics and the ...
Daud Ahmad +5 more
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