MATLAB Newton Raphson Storing Iterative Root Estimates

Question

I am looking for help to be able to store all my iterative root estimates and number of iterations in my MATLAB code. It is based off a pseudocode, but I am having trouble doing this because not all the data is in the for loop. I have attached my code below.

function [x] = Newton_savesteps(f,fp,x)

%define arr1, arr2, arr3 here

% Preallocating arrays

% n = [];

% x = [];

% f_x = [];

nmax = 500;

delta = 0.5*10^-6;

epsilon = 0.5*10^-6;

f_x = f(x);

disp([0,x,f_x])

% store values arr1(1) = ...

for n = 1:nmax

f_p = fp(x);

if abs(f_p) < delta

disp('small derivative')

return

end

d = f_x/f_p;

x = x-d;

f_x = f(x);

disp([n,double(subs(x)),double(subs(f_x))])

% store values

%arr1(n+1) = ...

if abs(d) < epsilon

disp('convergence')

x = double(subs(x));

return

end

end

x = double(subs(x));

end

Answer 1

function [x] = Newton_savesteps(f, fp, x)

% Parameters

nmax = 500;

delta = 0.5e-6;

epsilon = 0.5e-6;

% Initialize storage arrays

x_values = zeros(nmax, 1); % Array to store x values

f_x_values = zeros(nmax, 1); % Array to store f(x) values

f_x = f(x);

disp([0, x, f_x]);

% Store initial values

x_values(1) = x;

f_x_values(1) = f_x;

for n = 1:nmax

f_p = fp(x);

if abs(f_p) < delta

disp('small derivative');

return;

end

d = f_x / f_p;

x = x - d;

f_x = f(x);

% Store values

x_values(n+1) = x;

f_x_values(n+1) = f_x;

disp([n, x, f_x]);

if abs(d) < epsilon

disp('convergence');

return;

end

end

% Trim arrays to actual number of iterations performed

x_values = x_values(1:n+1);

f_x_values = f_x_values(1:n+1);

% Return the last value

x = x_values(end);

end