MATLAB: Please help, I wrote a matlab code for the Simple Subspace Iteration. But the iteration does not to stop

Here is the algorithm

Start: Choose an initial system of vectors X_{0}

Iterate: Until convergence do,

(a)X_{k}=AX_{k-1}

(b)X_{k}=QR the QR factorization of X_{k} and set X_{k}=Q

Here is my code

function [v,lamda] = SSI(A,tol) n=size(A,1); v=rand(n,1); res=1; while (res > tol) W= A*v; [Q,R]=qr(W); lamda=Q end

Best Answer

You have to calculate res in the while loop for it to end at some point.

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MATLAB: Problems in QR function

A = .... whatever is appropriate
for iteration = 1 : 1000
  [Q,R] = cgs(A);
end

This would not appear to make much sense to do unless you are changing A between iterations, or unless you are doing this in order to time the execution. If you are doing this for timing purposes then we would recommend that you instead use

timing = timeit(@() cgs(A), 2)

MATLAB: Multivariate Newton Method – Numerical Aproximation in Matlab

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!

Best Answer

Related Solutions

MATLAB: Problems in QR function

MATLAB: Multivariate Newton Method – Numerical Aproximation in Matlab

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