how to recursively code the bisection algorithm

This is how I'm trying to make the code recursive. But I have some errors:

Can you please haelp me?

[John D'Errico]

When you post a PICTURE of your code, nobody can help you without typing in the code by hand from that picture. This makes it significantly harder to help you, when all you needed to do was to paste in the TEXT directly.

Since text is trival to do, is there a good reason why you want to make it more difficult for you to get help?

[Dimitra]

ok i will do it!

Answer 1

[Tushar]

Hi Dimitra,

I think we can do it like this:

function root = bisection_recursive(f, a, b, tol, max_it)
    fa = feval(f, a);
    fb = feval(f, b);
    
    % Check if a root is already found
    if abs(fa) < tol
        root = a;
        return;
    elseif abs(fb) < tol
        root = b;
        return;
    end
    
    % Check if the interval is valid
    if fa * fb > 0
        error('No root exists in the given interval.');
    end
    
    % Recursive bisection algorithm
    function root = bisection_recursive_helper(a, b, x_previous, i)
        if i > max_it
            error('Maximum number of iterations reached.');
        end
        
        x = (a + b) / 2;  % Midpoint
        
        fprintf('Iteration %3d: %10.8f\n', i, x);
        
        fx = feval(f, x);
        
        if abs(x - x_previous) < tol || abs(fx) < tol
            root = x;
            return;
        end
        
        if fa * fx < 0
            root = bisection_recursive_helper(a, x, x, i + 1);
        else
            root = bisection_recursive_helper(x, b, x, i + 1);
        end
    end

    % Call the recursive helper function
    root = bisection_recursive_helper(a, b, b, 1);
end

To use this function, you need to define your function f and provide the initial interval [a, b], the tolerance tol, and the maximum number of iterations max_it. The function will recursively divide the interval and converge to the root within the specified tolerance or maximum number of iterations.

Here's an example of how you can use the bisection_recursive function to find the root of a function:

% Define your function
f = @(x) x^2 - 4;

% Define the interval [a, b]
a = 1;
b = 3;

% Set the tolerance and maximum number of iterations
tol = 1e-6;
max_it = 100;

% Call the bisection_recursive function
root = bisection_recursive(f, a, b, tol, max_it);

% Display the result
fprintf('Root: %10.8f\n', root);

Make sure to modify the function f and the input parameters a, b, tol, and max_it according to your specific problem.

[Dimitra]

Thank you very much! I will try it right now