CLOSED METHODS
A simple method to obtain an approximation to the root of the equation f(x)=0, is to plot the function and see where it crosses the X axis.
The graph shows the existence of several roots, including perhaps a double root around X = 4.2
Reducing the horizontal scale is obtained:
In fact there are two different roots X=4.23 and X=4.26
The Bisection Method
The bisection method, also known as cutting binary or interval partition of Bolzano, is a type of incremental search in which the interval is always divided in half. If the value of the function changes sign on an interval, we evaluate the function value at the midpoint. The root position is determined by placing the midpoint of the subinterval, in which case a change of sign. The process is repeated until a better aproximation.
Error Estimates
An objective criterion to define when a numerical method has to stop, is to estimate the error in a way that does not require prior knowledge of the root. As discussed above, one can calculate the percentage relative error T as follows:
Method of False Position
This is the equation of false position. The estimated value of Xr then to replace either baseline Xi or Xu.
OPEN METHODS
Simple Fixed Point Iteration
Use a simple iteration fixed point to locate the following:
Newton Raphson Method
Secant Method
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