A New Operational Matrix of Derivative for Orthonormal Bernstein Polynomial's

Abstract

In this paper, an orthonormal family has been constracted {b_i6 }_(i=0)^6 of polynomials of degree six is first constructed by using Gram-Schmidt orthonormalization process on Bernstein polynomials {B_i6 }_(i=0)^6.Then, an orthonormal Bernstein operational matrix of derivative D_b is derived.Finally, the orthonormal Bernstein expansions along with operational matrix of derivative are applied for variational problemsapproximately.