Generalized Tschebyscheff of the Second Kind and Bernstein Polynomials Change of Bases
نویسنده
چکیده
We constructmultiple representations relative to different bases of the generalized Tschebyscheff polynomials of second kind. Also, we provide an explicit closed from of The generalized Polynomials of degree r less than or equal n in terms of the Bernstein basis of fixed degree n. In addition, we create the change-of-basis matrices between the generalized Tschebyscheff of the second kind polynomial basis and Bernstein polynomial basis. 2010 Mathematics Subject Classifications: 42C05, 33C50, 33C45, 33C70, 05A10, 33B15
منابع مشابه
Generalized Tschebyscheff - Ii Weighted Polynomials on Simplicial Domain Mohammad
In this paper, we construct generalized Tschebyscheff-type weighted orthogonal polynomials U n,r (u,v,w), γ > −1, in the Bernstein-Bézer form over the simplicial domain. We show that U n,r (u,v,w), r = 0,1, . . . ,n; n= 0,1,2, . . . , form an orthogonal system over a triangular domain with respect to the generalized weight function.
متن کاملExpansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind
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...
متن کاملA solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
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.
متن کاملGeneralized Chebyshev polynomials of the second kind
We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the pap...
متن کاملNumerical resolution of large deflections in cantilever beams by Bernstein spectral method and a convolution quadrature.
The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...
متن کامل