Golden Section

clc;

clear;



f=@(x) x.^2+2*x;

a=-3;

b=3;

error=0.8;





r=(sqrt(5)-1)/2;



x0=a;

x3=b;

x1=a+(1-r)*(b-a);

x2=a+r*(b-a);



y1=feval(f,x1);

y2=feval(f,x2);





while (x3-x0)*r>error

if y1<=y2

x3=x2;

x2=x1;

x1=x0+(1-r)*(x3-x0);



else

x0=x1;

x1=x2;

x2=x0+r*(x3-x0);

end



y1=feval(f,x1);

y2=feval(f,x2);

end

y_array=[feval(f,x0),y1,y2,feval(f,x3)];

[ymin,index]=min(y_array);

x_array=[x0,x1,x2,x3];

xmin=x_array(index);



disp(sprintf('minimum of f(x) is %5.3f that occurs at x=%5.3f\n',ymin,xmin))