How do I use a for loop for the newton raphson method?

The code I have is where f is a function handle, a is a real number, and n is a positive integer:

function r=mynewton(f,a,n)
syms x
f=@x;
c=f(x);
y(1)=a;
for i=[1:length(n)]
y(i+1)=y(i)-(c(i)/diff(c(i)));
end;
r=y

The erros I am getting are:

Undefined function or variable 'x'.
Error in mynewton (line 4)
c=f(x);

How do I fix these errors?

[Alexander]

In line 3 you overwrite your input parameter f with @x. What do you want to achieve with this?

Answer 1

[arushi]

Hi Yo,

Here's the corrected version of your Newton's method implementation:

function r = mynewton(f, a, n)
    syms x
    % Symbolically define the function
    c = f(x);
    % Calculate the derivative of the function
    dc = diff(c);

    % Initialize the first guess
    y(1) = a;

    % Perform Newton's iteration
    for i = 1:n
        % Evaluate the function and its derivative at the current guess
        f_val = subs(c, x, y(i));
        df_val = subs(dc, x, y(i));
        
        % Update the guess using Newton's formula
        y(i+1) = y(i) - double(f_val) / double(df_val);
    end

    % Return all iterations
    r = y;
end

Hope this helps.