simple False Position code

I'm trying to do a simple False Position code following my teachers model but can't get it to actually work. Not sure if my if, else is wrong or what as it only says Method failed but I know there should be and answer of P=3.0571 and i=16. Totally new to programming and matlab so any help would be greatly valued. Thanks

%False Position %(x^2-4x+4-lnx=0 for 2<=x<=4)

p0=2; p1=4; TOL=10^-6; N=100;

q0=p0^2-4*p0+4-log(p0); q1=p1^2-4*p1+4-log(p1);

i=2; while i<=N p=p1-q1*(p1-p0)/(q1-q0);

    if abs(p-p1)<TOL
        disp('False Position')
        p
        i
        break
    end

     i=i+1;
    q=p^2-4*p+4-log(p);

    if q*q1<0
        p0=p1;q0=q1;
    else
        p1=p;q1=q;
    end
end

   if i>=N disp('Method Failed')
   end

Answer 1

[Roger Stafford]

I believe your error lies in the lines

if q*q1<0
  p0=p1;
  q0=q1;

They ought to read

if q*q1<0
  p0=p;
  q0=q;

The idea is to keep the signs of q0 and q1 opposite, so you set either (p1,q1) or (p0,q0) to (p,q) whichever will retain that as true while continually shrinking the interval length. You were setting (p0,q0) to (p1,q1) which would suddenly shrink the interval length to zero with the true solution off to one side.

Answer 2

[Ayana]

function [root, iter] = false_position(f, a, b, tol, max_iter) % f: function handle for which we want to find the root % a: lower bound of the interval % b: upper bound of the interval % tol: tolerance for convergence % max_iter: maximum number of iterations

    if f(a) * f(b) >= 0
        error('f(a) and f(b) must have different signs');
    end

    iter = 0;
    root = a; % Initialize root

    while iter < max_iter
        % Calculate the false position
        root = (a * f(b) - b * f(a)) / (f(b) - f(a));

        % Check if the root is close enough to zero
        if abs(f(root)) < tol
            break; % Found the root within tolerance
        end

        % Update the interval
        if f(root) * f(a) < 0
            b = root; % The root is in the left subinterval
        else
            a = root; % The root is in the right subinterval
        end

        iter = iter + 1; % Increment iteration count
    end

    if iter == max_iter
        warning('Maximum number of iterations reached without convergence.');
    end
end

▎How to Use the Function

1. Define your function as a function handle. For example, if you want to find the root of f(x) = x² - 4 :

      f = @(x) x^2 - 4;

2. Call the false_position function with appropriate arguments:

      a = 0; % Lower bound of the interval
   b = 5; % Upper bound of the interval
   tol = 1e-6; % Tolerance for convergence
   max_iter = 100; % Maximum number of iterations

   [root, iter] = false_position(f, a, b, tol, max_iter);
   fprintf('Root: %.6f found in %d iterations\n', root, iter);

f(x) = x² - 4  within the interval [0, 5]. Adjust the function, interval, tolerance, and maximum iterations as needed for your specific problem.

root=a; % initialize root