numerical methods. recurrence of iteration method

Question

Follow iteration method.
Xn+1 = Xn (Xn^2 +6) / (3Xn+2)

Can this method be used to approximate a root of f(x) =x^2-2.

Note Xn och Xn+1 are the cvariables.

Newtons formula are the following

om Xn+1 = Xn -f(Xn)/ f'(Xn)

So i should test from this equation and find f(x) and then see if its equal x^2 -2.

Anyone that ca help me with that?

Answer 1

Newton's method in computer form is x = x - f(x)/f'(x) or in this case x1= x0 - (x0^2 - 2) / (2*x0). In MATLAB12. 

% Newtons Method
x = zeros(1,10);
x(1,1) = 1.33;
for i = 1:10;
x(1,i+1) = x(1,i) - ((x(1,i)^2 - 2)) / (2*x(1,i));
end
disp(x(1,10));
end

This will give the the sqrt(2) correct to at least four places after several iterations. I don't know what your algorithm will produce or how you derived it. If the algorithm converges then Xn+1 = Xn. Upon substituting in the iteration Xn+1 = 0.

I don't think your algrithm converges.