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A new method of root finding is formulated that uses a numerical iterativeprocess involving three points. A given function y = f(x) whose roots aredesired is fitted and approximated by a polynomial function of the form P(x)=a(x-b)^N that passes between three equi-spaced points using the method of leastsquares. Successive iterations using the same procedure of curve fitting isused to locate the root within a given level of tolerance. The power N of thecurve suitable for a given function form can be appropriately varied at eachstep of the iteration to give a faster rate of convergence and avoid caseswhere oscillation, divergence or off shooting to an invalid domain may beencountered. An estimate of the rate of convergence is provided. It is shownthat the method has a quadratic convergence similar to that of Newton's method.Examples are provided showing the procedure as well as comparison of the rateof convergence with the secant and Newton methods. The method does not requireevaluation of function derivatives.

A three point formula for finding roots of equations by the method of least squares