Root finding

In the following example it will be shown how to create a Matlab script for the Root finding Newton-Rapson method. I personally encourage you to try and create scripts for the other two root-finding methods.

1. First define the function you want to analyse and their respective derivative.(This method requires the Symbolic Math Toolbox, it is possible to do it without but it is much quicker)

    f = @(x) x^2+4 - x^3;
    dfdx = diff(f,x)
   

2. Then declare the initial guess of your root and the number of trials. ```matlab:Code int_guess = 3; number_trials = 20
3. Before starting the loop we need to calculate the first guess of the approximation.

    root = int_guess - f(int_guess)/dfdx(int_guess)
   

4. Finally create a loop and perform the algorythm for the number of trials and display the root.

    for i = 1:number_trials
        root = root - f(double(root))/dfdx(double(root));
        double(root)
    end
   

Dyson School of Design Engineering 2021 - Ivan Revenga Riesco