-
161
Quantum (q, h)-Bézier surfaces based on bivariate (q, h)-blossoming
Published 2019-10-01“…We introduce the (q, h)-blossom of bivariate polynomials, and we define the bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces on rectangular domains using the tensor product. …”
Get full text
Article -
162
Bernstein collocation method for neutral type functional differential equation
Published 2021-04-01“…In this paper, we used a spectral collocation method which is based on Bernstein polynomials to find the approximate solution. The disadvantage of using Bernstein polynomials is that they are not orthogonal and therefore one cannot use the properties of orthogonal polynomials for the efficient evaluation of differential equations. …”
Get full text
Article -
163
Some properties and inequalities related to the kth inverse moment of a positive binomial variate
Published 2009-02-01“…Keywords: Probability, statistics, life contingencies, Bernstein polynomials.…”
Get full text
Article -
164
Approximation of Second-Order Moment Processes from Local Averages
Published 2009-01-01“…We also provide some insight and generalization of the connection between Bernstein polynomials and Brownian motion, which was investigated by Kowalski in 2006.…”
Get full text
Article -
165
Alternative methods for solving nonlinear two-point boundary value problems
Published 2018-06-01“…In this sequel, the numerical solution of nonlinear two-point boundary value problems (NTBVPs) for ordinary differential equations (ODEs) is found by Bezier curve method (BCM) and orthonormal Bernstein polynomials (OBPs). OBPs will be constructed by Gram-Schmidt technique. …”
Get full text
Article -
166
Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators
Published 2022-06-01“…An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. …”
Get full text
Article -
167
New results on the q-generalized Bernoulli polynomials of level m
Published 2019-12-01“…This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials Bn[m-1](x;q)B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.…”
Get full text
Article -
168
Fractional Bernstein operational matrices for solving integro-differential equations involved by Caputo fractional derivative
Published 2022-05-01“…The present work is devoted to developing two numerical techniques based on fractional Bernstein polynomials, namely fractional Bernstein operational matrix method, to numerically solving a class of fractional integro-differential equations (FIDEs). …”
Get full text
Article -
169
Bernstein-type approximations of smooth functions
Published 2007-10-01“…The Bernstein-type approximations generalize the corresponding Bernstein polynomials, by considering definitions that depend on a convenient approximation coefficient in linear kernels. …”
Get full text
Article -
170
Convolution Operators With Spline Kernels
Published 1994“…These formulas are analogous to the Bernstein's extension of Voronovskaya's estimate for Bernsteins polynomials and Marsden and Riemenschneider's extension of Bernstein-Schoenberg operators for higher order derivatives.…”
Get full text
Thesis -
171
Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems
Published 2021-09-01“…Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.…”
Get full text
Article -
172
A simplified method to approximate a ROC curve with a Bézier curve to calculate likelihood ratios of quantitative test results
Published 2020-01-01“….• Here, we make use of cubic Bézier curves defined by Bernstein polynomials of degree 3.• A simplified method to adjust a Bézier curve to a ROC curve is presented• The crucial advantage of this procedure is that Bézier curves are constructed by tangents to the ROC curve, whose slopes immediately provide the LR of a specific point on the curve.…”
Get full text
Article -
173
A numerical comparative analysis of methods for solving fractional differential equations
Published 2024-12-01“…AbstractIn this paper, we present two collocation methods utilizing subdivision schemes and Bernstein polynomials as their basis functions to solve Caputo-type fractional differential equations. …”
Get full text
Article -
174
Computation of numerical solutions to variable order fractional differential equations by using non-orthogonal basis
Published 2022-04-01“…For the said numerical analysis, we use Bernstein polynomials (BPs) with non-orthogonal basis. The method we use does not need discretization and neither collocation. …”
Get full text
Article -
175
Asymptotic Frame Fields of Rational Bézier Curves
Published 2021-12-01“…The curves can be defined with the help of De Casteljau algorithm, which is one of the most basic elements of curve and surface design, and Bernstein polynomials, which facilitate theoretical developments. …”
Get full text
Article -
176
Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems
Published 2023-01-01“…. • This method involves computing numerical eigenvalues using Bernstein polynomials as the basis functions. • The novel weighted residual Galerkin technique's performance is numerically validated by comparing it to other numerical/analytical approaches in the literature.…”
Get full text
Article -
177
A new closed form method for design of variable bandwidth linearphase FIR filter using different polynomials
Published 2014“…In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response(FIR) filters using different polynomials such as shifted Chebyshev polynomials, Bernstein polynomi-als and shifted Legendre polynomials is proposed. …”
Get full text
Article -
178
Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods
Published 2023-10-01“…The proposed empirical checkerboard copula within a hierarchical empirical Bayes model alleviates the aforementioned issues and provides a smooth estimator based on multivariate Bernstein polynomials that itself is shown to be a genuine copula. …”
Get full text
Article -
179
On Degenerate Truncated Special Polynomials
Published 2020-01-01“…In addition, regarding applications, by introducing the degenerate truncated forms of the classical Bernstein polynomials, we obtain diverse correlations and formulas. …”
Get full text
Article -
180
Bernstein spectral method for quasinormal modes and other eigenvalue problems
Published 2023-12-01“…In this work we highlight the usefulness of a relatively unknown set of non-orthogonal basis functions, known as Bernstein polynomials, and their advantages for handling boundary conditions in ordinary differential eigenvalue problems. …”
Get full text
Article