Use while for bisection method

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Omed Zewar
Omed Zewar 2017-12-5
回答： Kautuk Raj 2023-6-2
Hi i want a program to bisection method by while
  2 个评论
Walter Roberson
Walter Roberson 2017-12-5
That is the normal method of programming bisection method. You can find a number of postings about bisection method if you search.
Vidhi Agarwal
Vidhi Agarwal 2023-6-2
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);

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回答（1 个）

Kautuk Raj
Kautuk Raj 2023-6-2
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);

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