Answer to Question #236456 in MatLAB for kay

Question

Modify the power method so that the stopping condition is changed to

| ((Ax_n-u_n x_n)/|X_n|) | <tolerance

where xn, μn are the current estimates of the eigenvector and eigenvalue. Demonstrate the validity of your code by running it on the matrix

3 -1 0

-1 2 -1

0 -1 3

Answer 1

A = gallery('circul',3)
[V,D] = eig(A)
[d,ind] = sort(diag(D))
Ds = D(ind,ind)
Vs = V(:,ind)
e1 = norm(A*V-V*D);

e2 = norm(A*Vs-Vs*Ds);

e = abs(e1 - e2)