A Probabilistic Dual-Fusion Version of Bernsteinís Polynomial Approximation Operator

by Ashok Sahai.

Abstract: The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not only provided an interesting proof of the Weierstrassí theorem, but also displayed a sequence of the polynomials which approximate the given function f (x) ? C[0, 1]. A probabilistic ĎDual-Fusioní version of Bernsteinís Polynomial Operator is proposed. The potential of the aforesaid improvement algorithm is tried to be brought forth and illustrated through an empirical study for which the function is assumed to be known in the sense of simulation.

Key Words: Approximation; Bernstein operator; Simulated empirical study

Ashok Sahai, sahai.ashok@gmail.com

Editor: A.M. Abd-Elfattah,a_afattah@hotmail.com

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