Efficient Quadrature Using Bernstein’s Polynomial Weights via Fusion of Two Dual-Perspectives

Abstract

A new polynomial quadrature operator has been proposed which uses weight-functions of the well-known Bernstein’s Polynomial operator in its improved structure, achieved through a rather-ingenious ‘Fusion’ of two dual perspectives. These weights are functions of the impugned variable of the unknown function being approximated, and are not mere constants. The new quadrature formula has been compared empirically with that quadrature using the well-known “Bernstein Operator”. The percentage absolute relative errors for the proposed quadrature formula and that with the “Bernstein Operator” have been computed for certain selected functions and with different number of node points in the interval of quadrature. It has been observed that the proposed quadrature formula produces exceedingly-significantly better results.