# I am not seeing what is wrong with my code, I've checked doc and help.

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James T on 15 Sep 2017
Edited: James Tursa on 18 Sep 2017
function [ root, error_bound ] = bisection(f, a0, b0, ep, max_iterate)
%function bisection(f, a0, b0, ep, max_iterate)
%This is the bisection method for solving an equation f(x)=0.
% Input:
% f: function to find root.
% a0: Left endpoint of initial interval.
% b0: Right endpoint of initial interval.
% ep: Error tolerance.
% max_iterate: Maximum iterates in loop, in case the code has an
% infinite cycle.
% Output:
% root
% error_bound
% =================Initializing=====================
root = 0;
error_bound = 0;
% ==================================================
% ============= YOUR CODE BEGINS HERE ==============
a = a0;
b = b0;
for n = 0:max_iterate
c = (a + b) / 2;
if b - c <= ep
disp('c is the root')
break;
end
if sign(f(b)) * sign(f(c)) <= 0 %%this is where I am having an issue but I am sure this is right%%
a = c;
else
b = c;
return
end
root = c;
error_bound = b - c;
% ============== YOUR CODE ENDS HERE ===============
end
##### 2 CommentsShowHide 1 older comment
James T on 16 Sep 2017
so, after reading what you showed me, is this the code I am looking for?
if sign(f(a0))*sign(f(b0)) > 0
return
end
for n = 1:max_iterate
c = (a0 + b0) / 2;
if b0 - c <= ep
break;
end
if sign(f(b0)) * sign(f(a0)) <= 0
a0 =c;
else
b0 = c;
end
end
root = c;
error_bound = b0 - c;

James Tursa on 15 Sep 2017
You have an inadvertent return statement:
else
b = c;
return <-- get rid of this line
The way you have it now, the first time you enter this branch the function returns without doing any more bisection iterations.
##### 2 CommentsShowHide 1 older comment
James Tursa on 18 Sep 2017
I like the fact that you have added a check to see that the inputs have bracketed the root. However, for this case I would advise generating an error instead of returning with bogus 0 values. E.g.,
if sign(f(a0))*sign(f(b0)) > 0
error('Inputs do not bracket the root');
end
You might also think about other issues to check for. E.g., what happens if a0 > b0 on input? What happens if ep < 0 on input? Etc.
But you have changed your working middle point check for an incorrect test. I.e., you have changed this line, which correctly tests where c is:
if sign(f(b)) * sign(f(c)) <= 0
for this test, which doesn't test c at all:
if sign(f(b0)) * sign(f(a0)) <= 0
Why did you make that change? Go back to the form of the original test which was working to test which side of the root c is on.