An Iterative Algorithm Using the Statistical Perspective of Bias for Efficient Polynomial Approximation by Modified MKZ Operator

by Robin Antoine andAshok Sahai.

Abstract: This paper aims at constructing an iterative computerizable numerical algorithm for an improved polynomial approximation by a modified version of ‘MKZ’ operator. The algorithm uses the ‘Statistical Perspective of Bias’ for exploiting the information about the unknown function ‘f’ available in terms of its known values at the ‘pre-chosen-knots’ in C [0, 1/2] more fully with the proposed modified operator. The improvement, achieved by an a-posteriori use of this information, happens iteratively. Any typical iteration uses the typical concepts of ‘Bias’. The potential of the achievable efficiency through the proposed ‘computerizable numerical iterative algorithm’ is illustrated per an ‘empirical study’ for which the function ‘f’ is assumed to be known in the sense of simulation. The illustration has been confined to “Three Iterations” only, for the sake of simplicity of illustration.

Key Words: Approximation; simulated empirical study

Authors:
Robin M. Antoine, rmantoine@hotmail.com
Ashok Sahai, sahai.ashok@gmail.com

Editor: Ahmed H. Youssef,ahyoussef@hotmail.com

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