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r = 3 − 5 (5.29)
2

and hence, the name of the method.
The following function M-file implements the above algorithm:

function [xmin,ymin]=goldensection(funname,a,b,
tolerance)
r=(3-sqrt(5))/2;
c=a+r*(b-a);
fc=feval(funname,c);
d=a+(1-r)*(b-a);
fd=feval(funname,d);
while d-c>tolerance
if fc>=fd
dnew=c+(1-r)*(b-c);
a=c;
c=d;
fc=fd;
d=dnew;
fd=feval(funname,dnew);

else
cnew=a+r*(d-a);
b=d;
d=c;
fd=fc;
c=cnew;
fc=feval(funname,cnew);
end
end

xmin=(c+d)/2;
ymin=feval(funname,xmin);

For example, if we wanted to find the position of the minimum of the
cosine function and its value in the interval 3 < x < 3.5, accurate to 10 , we
–4
would enter in the command window, after having saved the above function
M-file, the following command:

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