Bernstein, Operator And Its Iterative Linear Combination Of Structure And High Precision Interpolation Operator

Bernstein polynomails were first used by Bernstein in his constructive proof for the Stone-Weierstrass approximation theorem. Bernstein polynomials are still widely applied in computer-aided geometric design(CAGD), approximation theory and financial mathematics due to its good properties. However, its convergence rate is not very satisfactory and many scholars did much work to improve it. This article mainly discusses how to get a more accurate approximation by making full use of the linear combination of Bernstein operator and its iteration. Our new operator is better than the Boolean sum of Bernstein operator in some cases.