On Matrix Representation of Bernstein Polynomials for Triple Sequences

A companion matrix resultant for Bernstein polynomials

Matrix methods for the simplicial Bernstein representation and for the evaluation of multivariate polynomials

In this paper, multivariate polynomials in the Bernstein basis over a simplex (simplicial Bernstein representation) are considered. Two matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented. Also matrix methods for the calculation of the Bernstein coefficients over subsimplices generated by subd...

On the Fermionic p-adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials

Throughout this paper, let p be an odd prime number. The symbol, p, p , and p denote the ring of p-adic integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of p , respectively. Let be the set of natural numbers and ∪ {0}. Let νp be the normalized exponential valuation of p with |p|p p−νp p 1/p. Note that p {x | |x|p ≤ 1} lim← N /p p. ...

A 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.

Matrix Representation for the Beta Type Polynomials

The aim of this paper is to study and investigate some new properties of the beta polynomials. Taking derivative of the generating functions for beta type polynomials, we give two partial differential equations (PDEs). By using these PDEs, we derive derivative formulas of the beta type polynomials. In order to construct a matrix representation for the beta polynomials, we firstly show that the ...