• AN ITERATIVE REDUCED-BIAS ALGORITHM FOR A DUAL-FUSION VARIANT OF BERNSTEIN’S OPERATOR

Abstract

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 Weierstrass’ theorem, but also displayed a sequence of the polynomials which approximate the given function f (x) ε C[0, 1]. This paper is motivated by the “Iterative Statistical Bias-Reduction Strategy” proposed in Sahai (2004) for the Bernstein’s Polynomial Approximation operator. A ‘Dual-Fusion’ version of the Bernstein’s Polynomial Operator is proposed. This version has a ‘Systematic-Bias’ in approximation which is much more accessible to the ‘Iterative Algorithm’ of ‘Statistical Bias-Reduction’ proposed in Sahai (2004).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.