This study presents an improvement to the secant method by reconstruction, in numerical analysis,the secant
method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root
of a function F .The secant method can be thought of as a finite difference approximation of Newton’s
method. However the method was developed independently of Newton’s method and predated the latter by
over 3000 years.
Secant method which its convergence is superlinear is used in combination with bisection and inverse
quadratic interpolation in Brent’s and Zhang’s method wich are one of the most powerful root finding
algorithms.the new method presented in this study represents so much advantages in root finding algorithm
for non-linear equations, compared to the secant method , this uses secant lines from 2 circles in each
iteration, it then requires only one initial guess and its convergence is quadratic, this new method could
replace the secant method in Brent’s and Zhang’s method to make the algorithm more quick and more
efficient,some experimental tests presented in this study compares the performance of this new method to
the secant method.

you can see the file below:

marouane’s method