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Operational matrices of Bernstein polynomials and their applications. (English) Zbl 1195.65061
Summary: The Bernstein polynomials (B-polynomials) operational matrices of integration P, differentiation D and product C ^ are derived. A general procedure of forming these matrices are given. These matrices can be used to solve problems such as calculus of variations, differential equations, optimal control and integral equations. Illustrative examples are included to demonstrate the validity and applicability of the operational matrices.
MSC:
65F30Other matrix algorithms
65D32Quadrature and cubature formulas (numerical methods)
65D25Numerical differentiation
65K10Optimization techniques (numerical methods)
65L05Initial value problems for ODE (numerical methods)
65R10Integral transforms (numerical methods)