Writing code for bisection method; then storing values for each iteration of the loop.

Hello, I am trying to write a code for bisection method for a class project. I cant figure out why my code wont finish running and give me the root. I also need to store the values of a, b, c, x, and y for each iteration to plot them and make a table with? Can anybody help? Thank you.

clear; clc;
f=@(x)2 * x^4 +3 * x^3 - 11 * x^2 - 9 * x + 15 ; 
 
a=input('\n Enter left point of interval '); 
b=input('\n Enter right point of interval '); 
toll= 1e-10;  
err=abs(b-a);
c = ( a + b )/2;

if f(a) *f(b) > 0 
    disp 'Enter valid interval!!!');
else
    c = ( a + b) /2;
    toll= 1e-2;  
    err=abs(b-a);
    while err > toll
        if f(c) == 0
            fprintf( 'The Root is: %4.4f\n', c)
        else 
            c = ( a + b )/2;
            x = abs( b - c);
            y = abs(f(c));
            
            if ( f(a) * f(c)) <= 0
                c = b;
            else
                if ( f(b) * f(c)) <= 0
                    a = c;
                end
            end
        end
    end
end

Answer 1

[Geoff Hayes]

Bradley - look closely at the condition for the while loop

while err > toll

. Since toll (the tolerance) is fixed, how or where does err get set? You initialize it on the previous line but never reset this variable using the new a and b. A couple of other things:

• try and avoid using something like f(c) == 0 when comparing floats/doubles. Try a tolerance check instead similar to abs(f(c)) < eps.
• only iterate for a maximum number of iterations so that you don't get stuck in the while loop: so either iterate until the error is less than the tolerance OR unti the max number of iterations has been reached.
• use arrays to store values that you may want to plot outside of the loops.

[Bradley Johnson]

I got the program to work, thank you for your help.

How would i go about using arrays to stroe the values?

[Geoff Hayes]

Suppose that you allow for 100 maximum iterations for your loop. Then for x and y you could do

maxIterations = 100;
atIter = 0;
x = zeros(maxIterations,1);
y = zeros(maxIterations,1);
while err > toll && atIter <= maxIterations
    atIter = atIter + 1;
    if f(c) == 0
        fprintf( 'The Root is: %4.4f\n', c)
    else 
        c = ( a + b )/2;
        x(atIter) = abs(b - c);
        y(atIter) = abs(f(c));
        
        if ( f(a) * f(c)) <= 0
            c = b;
        elseif ( f(b) * f(c)) <= 0 % combined the else and if into an elseif
            a = c;
        end
    end
end