# Bisection method relative error

34 views (last 30 days)
Sazcl on 17 Mar 2022
Edited: Mohammed Hamaidi on 18 Mar 2022 Hello everyone, I don't use MATLAB very well. I have a question. If you can help, I'd appreciate.
I have a function below that I have to find its roots using bisection method. I want the for loop to stop on the point where relative error is lower than %0.05. I couldn't understand how I can define n.
f=@(x) log(x)-cos(x)-exp(-x);
x1=1;
x2=2;
xmid=(x1+x2)/2
for i=1:n;
if (f(xmid)*f(x2))<0
x1=xmid;
else
x2=xmid;
end
xmid=(x1+x2)/2;
end
fprintf('The root is: %3.8g\n',xmid)

Mohammed Hamaidi on 17 Mar 2022
Edited: Mohammed Hamaidi on 18 Mar 2022
Hi
Just use "while" loop with your condition as follows:
f=@(x) log(x)-cos(x)-exp(-x);
x1=1;
x2=2;
xmid=(x1+x2)/2;
while (x2-x1)>0.0005
if (f(xmid)*f(x2))<0
x1=xmid;
else
x2=xmid;
end
xmid=(x1+x2)/2;
end
fprintf('The root is: %3.8g\n',xmid)
Jan on 18 Mar 2022
If this answer solves the problem, please accept it.

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