#truex = linspace(0,1,20);
#x0=[0,1/3,1/2,1]
#f=@(x)cos(pi*x);

#plot(x0, f(x0),'o');
#hold on

#plot(truex, f(truex),'blue');


#lnf = newton(x0,f(x0),truex)

#plot(truex, lnf, 'r');

#lnf = newton(x0,f(x0),1/5)

#truex = linspace(1001,1009,9);

#x0=[1000,1010,1020,1030,1040,1050];
#f0=[3.000000,3.0043214,3.0086002,3.0128372,3.0170333,3.0211893];

#lnf = newton(x0,f0,truex)


x0 = linspace(-4,4,9);
f=@(x)power(2,x);

lnf = aitken(x0,f(x0),1/2)