orthogonal iteration

also called subspace iteration or simultaneous iteration
it let us compute n dimensional rather one by each time

equivalent to QR iteration

Steps

start with and repeat following for

by QR factorization
when , we say it converge and stop

After convergence:

1. Compute the Rayleigh quotient matrix: where is last
2. Find eigen-decomposition of H: , where D is diagonal
3. Compute eigenvectors of original matrix A:
4. The diagonal entries of are the corresponding eigenvalues