A Two-phase Iterative Algorithm for Improved Approximation by Szasz Operator Using Statistical Perspectives

  •  Ashok Sahai    
  •  Robin Antoine    
  •  Peter S. Chami    


This paper aims at constructing a two-phase iterative numerical algorithm for the improved approximation of a continuous
function by the ‘Modified Szasz’ operator. The algorithm uses a ‘statistical perspective’ to more fully expoit the information
about the unknown function f . The improvement occurs iteratively. A typical iteration uses the twin statistical
concepts of ‘Mean Square Error’ (MSE) and ‘Bias’; the application of the latter concept being preceded by that of the
former in the algorithm. At any iteration, the statistical concept of ‘MSE’ is used in “Phase II”, after that of the ‘Bias’ in
“Phase I”. The procedure is like a sandwich. The top and bottom slices are the operations of ‘Bias-Reduction’ in “Phase
I” of the algorithm, and the operation of ‘MSE-Reduction’ in “Phase II” is the stuffing in the sandwich. The improvement
acheived by this algorithm is evaluated by means of a simulation study using known functions. The simulation has been
confined to three iterations only, for the sake of simplicity.

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