Wegstein's Method for solving non-linear equations

This code employs the Wegstein's method to solve non-linear equations.

Solving non-linear equations can be troublesome and many of the existing methods can diverge, or might be sensitive to initial guesses. Other methods would require the calculation of the derivative of the function. The Wegstein's method is a modification to the fixed-point method for solving non-linear equations, which does not require the calculation of any derivatives, and it is pretty insensitive to initial guesses. Refer to the following for more information on the method:

https://ir.library.oregonstate.edu/downloads/2r36v1962

https://www.youtube.com/watch?v=T_6mR6rJXQQ