Aim of the applet

Interpret geometrically the approximations of a root constructed by means of the algorithm. Analyze the convergence according to the information of entry.

Input data

Via keyboard:


• Function f(x).
• Function g(x).
• Starting point of the algorithm, Xo.
• Tolerance and maximum number of steps.

Via graph:


• The starting point of the algorithm. It can modify over the graph with the mouse.

Output data

Graphical representation of the functions f, g and the line y = x.

Results table and final relative error.

First steps

Find a root of f, given by f (x) = x ^ 3 as a fixed point of g, where g (x) = (x +1) ^ (1 / 3). Change the value of x0 with the mouse and see how it changes the number of iterations. Also analyze the effect of decreasing the maximum relative error.

Change the function g to find the same root and analyzes the convergence in both cases.