On Orthonormal Bernstein Polynomial of Order Eight
[1]
Suha N. Shihab , Applied Science Department, University of Technology, Baghdad, Iraq.
[2]
Tamara N. Naif , Applied Science Department, University of Technology, Baghdad, Iraq.
In this paper, we present the new orthonormal base 〖OB〗_(i,8),i=0,1,…,8 through the Gram-Schmidt Orthonormalization process on Bernstein polynomials of order eight. Bernstein polynomials and their properties are employed to derive explicit formulas for derivative and integration operational matrices of orthonormal Bernstein polynomials of order eight. Convergence criteria is also included in this paper. The relationship between the derivative of 〖OB〗_(i,8) and B_(i,8) themselves with some other important properties are derived in this work. All the proposed results are of direct interest in many applications.
Bernstein Polynomials, Gram- Schmidt Orthonormalization Process, Operational Matrix of Derivative and Integration
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