ON CONSTRUCTING A HIGHER-ORDER EXTENSION OF DOUBLE NEWTON'S METHOD USING A SIMPLE BIVARIATE POLYNOMIAL WEIGHT FUNCTION

Abstract

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter γ and a weight function H(s, u). We have determined forms of γ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

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