Plotting Bisection intervals code

Looking for where I plot the intervals on a `plot()` and where ?

function [x,e] = MyBisectFunc(f, a1,b1, number)

format long

c1 = f(a1); d1 = f(b1);

if c1*d1 > 0.0

error ('Func has same sign at both endpoints')

end

for i = 1:number

x = (a1 + b1) /2;

y = f(x);

disp([x,y])

% tried this but nothing showed up on the graph

plot(x,y)

if abs(y) < 10^-8

break

end

if c1*y < 0

b1 = x;

else

a1 = x;

end

end

x = (a1 + b1)/2;

e = (b1 - a1) /2;

Answer 1

[Aashray]

Hello @gracias claude,

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:

1. Plot the function once for reference
2. 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:

Answer 2

[Harshavardhan]

Hi @gracias claude

In MATLAB, the “plot(x, y)” command plots a single point or line segment, but it does not automatically retain previous points plotted in a loop. To continuously update the plot with each iteration, you need to use the "hold on” command, which tells MATLAB to retain the current plot and add new data to it.

To fix the issue:

1. Add the following lines before the “for” loop:

figure; hold on; grid on;
xlabel('x'); ylabel('f(x)');
title('Bisection Method Iterations');

2. Replace “plot(x,y)” with:

plot(x, y,'ro'); % red circle for each iteration

For more information on “plot” and “hold” refer to their respective links below:

https://www.mathworks.com/help/matlab/ref/plot.html

https://www.mathworks.com/help/matlab/ref/hold.html