In this paper we propose using planar and spherical Bernstein polynomials over triangular domain for radiative transfer computations. In the planar domain, we propose using piecewise Bernstein basis functions and symmetric Gaussian quadrature formulas over triangular elements for high quality radiosity solution. In the spherical domain, we propose using piecewise Bernstein basis functions over ...

A scheme for constructing orthogonal systems of bivariate polynomials in the Bernstein–Bézier form over triangular domains is formulated. The orthogonal basis functions have a hierarchical ordering by degree, facilitating computation of least-squares approximations of increasing degree (with permanence of coefficients) until the approximation error is subdued below a prescribed tolerance. The o...

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logari...

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[0,1]. We define the weighted dual functionals of the Bernstein polynomials, which are used to find the coefficients in the least squares approximation. 2006 Elsevier Inc. All rights reserved.

In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

In this paper, the order of simultaneous approximation and Voronovskaja type theorems with quantitative estimate for complex genuine q-Bernstein-Durrmeyer polynomials (0 < q < 1) attached to analytic functions on compact disks are obtained. Our results show that extension of the complex genuine q-Bernstein-Durrmeyer polynomials from real intervals to compact disks in the complex plane extends a...

In this paper, when approximating a continuos non-negative function on the unit interval, we present an alternative way to the classical Bernstein polynomials. Our new operators become nonlinear, however, for some classes of functions, they provide better error estimations than the Bernstein polynomials. Furthermore, we obtain a simultaneous approximation result for these operators. 2010 Mathem...

An accurate method is proposed to solve problems such as identification, analysis and optimal control using the Bernstein orthonormal polynomials operational matrix of integration. The Bernstein polynomials are first orthogonalized, normalized and then their operational matrix of integration is obtained. An example is given to illustrate the proposed method. Mathematics Subject Classification: ...