| Abstract |
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A new quadrature formula has been proposed which uses modified weight functions derived from those of ‘Bernstein Polynomial’ using a ‘Two-Phase Modification’ therein. The quadrature formula has been compared empirically with the simple method of numerical integration 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, with different number of usual equidistant node-points in the interval of integration~ [0, 1]. It has been observed that both of the proposed modified quadrature formulae, respectively after the ‘Phase-I’ and after the ‘Phases-I & II’ of these modifications, produce significantly better results than that using, simply, the “Bernstein Operator”. Inasmuch as the proposed “Two-Phase Improvement” is available iteratively again-and-again at the end of the current iteration, the proposed improvement algorithm, which is ‘Computerizable’, is an “Iterative-Algorithm”, leading to more-and-more efficient “Quadrature-Operator”, till we are pleased! |
