Efficient Approximation Using Probabilistically Improved Combinatorial Structure of Bernstein's Polynomial Operator's Weights through the Fusion of Dual-Perspectives (original) (raw)

2011, Journal of Mathematics Research

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The weighted dual functionals for the univariate Bernstein basis

Applied Mathematics and Computation, 2007

We find an explicit formula for the weighted dual functions of the Bernstein polynomials with respect to the Jacobi weight function using the usual inner product in the Hilbert space L 2 [0, 1]. We define the weighted dual functionals of the Bernstein polynomials, which are used to find the coefficients in the least squares approximation.

Gauss–Lobatto to Bernstein polynomials transformation

Journal of Computational and Applied Mathematics, 2008

The aim of this paper is to transform a polynomial expressed as a weighted sum of discrete orthogonal polynomials on Gauss-Lobatto nodes into Bernstein form and vice versa. Explicit formulas and recursion expressions are derived. Moreover, an efficient algorithm for the transformation from Gauss-Lobatto to Bernstein is proposed. Finally, in order to show the robustness of the proposed algorithm, experimental results are reported.

Bernstein polynomials and stochastic computing Polinomios de Bernstein y codificación estocástica de la información

2020

Among the multiples applications of Bernstein polynomials there is one related to the processing of random signals, originally introduced by John von Neumann in 1956. Thanks to advances in technology, some ideas from the late sixties of the last century have been retaken in order to design implementations which allow -in certain casesa simpler and more efficient processing than the traditional one. In this descriptive review article we will illustrate the use and importance of Bernstein polynomials in solving problems associated with stochastic computing, taking as a starting point the notion of stochastic logic in the sense of Qian-Riedel-Rosenberg.

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