Use while for bisection method

Hi i want a program to bisection method by while

[Walter Roberson]

That is the normal method of programming bisection method. You can find a number of postings about bisection method if you search.

[Vidhi Agarwal]

Please find the attached Bisection method code using while loop

You can also refer to this article for reference

(https://in.mathworks.com/matlabcentral/answers/755384-help-with-simple-bisection-method-function-while-loop)

% Define the function f(x)
f = @(x) x^3 - 1.6*x^2 - 2.4*x + 0.3;

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

% Define the tolerance (the maximum error allowed)
tol = 1e-6;

% Set the maximum number of iterations
max_iter = 1000;

% Initialize the variables
iter = 0;
midpoint = (a + b) / 2;
fa = f(a);
fb = f(b);

% Use a while loop to iteratively refine the midpoint
while abs(f(midpoint)) > tol && iter < max_iter
    midpoint = (a + b) / 2;
    fm = f(midpoint);
    if fm == 0
        break;
    elseif sign(fm) == sign(fa)
        a = midpoint;
        fa = fm;
    else
        b = midpoint;
        fb = fm;
    end
    iter = iter + 1;
end

% Display the results
fprintf('The midpoint of the function f(x) = x^3 - 1.6x^2 - 2.4x + 0.3 is: %f\n', midpoint);

Answer 1

[Kautuk Raj]

The bisection method is a numerical algorithm used to find the roots of a function within a specified interval. This is an example code in MATLAB that implements the bisection method:

% Define the function to find the root of
f = @(x) x^3 - 2*x - 5;
% Define the interval to search for the root in
a = 2;
b = 3;
% Set the tolerance and maximum number of iterations
tol = 1e-6;
max_iter = 100;
% Initialize the iteration counter and the bracketing interval
n_iter = 0;
c = (a + b) / 2;
% Loop until the desired tolerance or maximum number of iterations is reached
while abs(f(c)) > tol && n_iter < max_iter
    % Evaluate the function at the midpoint of the interval
    c = (a + b) / 2;
    fc = f(c);
    % Check which half of the interval to keep and update the interval
    if fc*f(a) < 0
        b = c;
    else
        a = c;
    end
    % Update the iteration counter
    n_iter = n_iter + 1;
end
% Display the result
fprintf('Root found after %d iterations: %f\n', n_iter, c);