function xc=bisect(f,a,b,tol)
% Bisection Method, xc=bisect(f,a,b,tol)
%  Computes an approximation to f(x)=0 given that the
%  root is bracketed in [a,b] with f(a)f(b)<0.  Will run
%  until TOL is reached, and will output the solution xc.
%
% EXAMPLE:  f=inline('x^3+x-1');
%          xc=bisect(f,0,1,0.00005);

%Error check and initialization:
fa=feval(f,a);  fb=feval(f,b);
if sign(fa)*sign(fb)>=0
    error('Root may not be bracketed');
end

iter=0;
while (b-a)/2>tol
    iter=iter+1;
    c=(a+b)/2;
    fc=feval(f,c);
    if fc==0  %This means that (a+b)/2 is the root-
        break     %Break out of the while loop and
                  %continue execution
    end
    if sign(fc)*sign(fa)<0  %New interval is [a,c] (reset b)
        b=c; fb=fc;
    else
        a=c; fa=fc;   %New interval is [c,b] (reset a)
    end
end
fprintf('Finished after %d iterates\n',iter);
xc=(a+b)/2;