Hi. I understand that you are trying to use the Newton Method to approximate eigenvalues and eigenvectors. I am assuming you are using the same method as it is described here. The goal for the Newton’s method is to approximate an eigenvalue and a corresponding eigenvector through updating the vector x, and vector v in your case, iteratively. In the code you provided, since the start of the for loop is defined after the calculation of vector v as well as the vector y and matrix J, these values will not be updated in each iteration. To fix this you should move the start of the for loop to the beginning of your function. Here is the modified code:
%Definition of Matlab function
function [y]=newZ(n,x,B)
%Using loop to end iteration as to error
for k=1:n % <-----------move your for loop to here
%Creating eigenvector as v=(v(1),v(2),v(3),v(4))
v=zeros(4,1);
v(1)=x(1);
v(2)=x(2);
v(3)=x(3);
v(4)=x(4);
%Defining function as desired to be
y=[B*v-x(5)*v;v'*v-1];
J=[B-x(5)*eye(4) -v; 2*v' 0];
if max(abs(y))>1e-4
x=x-J\y
else
break
x
end
end
end
Hope this helps!
