I understand that you have implemented the bisection interval method for finding approximate roots. And that you are trying to plot how the interval [a, b] changes with each iteration, along with the midpoints. Here is how you can achieve that:
- Plot the function once for reference
- Add dynamic interval and mid-point plotting in the loop
function [x, e] = MyBisectFunc(f, a1, b1, number)
format long
c1 = f(a1); d1 = f(b1);
if c1 * d1 >= 0
error('Func has same sign at both endpoints or a root at endpoint');
end
figure
hold on
grid on
xlabel('x')
ylabel('f(x)')
title('Bisection Method Convergence')
% Plot the function for reference
x_vals = linspace(a1, b1, 500);
plot(x_vals, f(x_vals), 'k--', 'DisplayName', 'f(x)')
tol = 1e-8; % Tolerance for interval size
for i = 1:number
x = (a1 + b1) / 2;
y = f(x);
% Plot current midpoint, ensuring it persists
plot(x, y, 'ro', 'MarkerSize', 8);
delete(findobj('Type', 'line', 'Color', 'b'));
plot([a1, b1], [0, 0], 'b-', 'LineWidth', 1.5);
drawnow
if abs(y) < 1e-8 || (b1 - a1) / 2 < tol
break
end
if c1 * y < 0
b1 = x;
else
a1 = x;
end
pause(0.5);
end
x = (a1 + b1) / 2;
e = (b1 - a1) / 2;
end
f = @(x) x.^3 - 2;
[x_root, error_est] = MyBisectFunc(f, 1, 2, 25);
I have also attached the plots that I obtained by using the above code:
