How to FAST calculate 2 norm / spectral norm of a matrix.

Question

I meant reduced 2 norm, the largest singular value.

My current approach is applying the SVD decomposition of A via "?gesdd" in MKL, and then taking the largest singular value.

I think there should be faster algorithm, since we only need the largest singular value.

By the way, my matrix is dense.

Answer 1

Try Arnoldi Iteration if you only need the largest singular value. Usually it converges very fast.

Search Arnoldi iteration in Wikipedia. It's not easy to write it here.