Calculate norm of A without densifing it

[EnLAI111]

Some algorithms need the l2-norm of A to calculate their step size. When A is used to convolve, I get its norm by np.linalg.norm(np.A @ np.identity(A.shape[1]), ord=2). We wonder if there is a way of calculation without densifing A.

[agramfort]

try this:

import numpy as np

A = np.random.rand(10, 10)
A = A.T @ A

lc = np.linalg.norm(A, ord=2)
print(lc)

def power_iteration(A, n_iter=500):
    x = np.random.randn(A.shape[0])
    for _ in range(n_iter):
        x = A @ x
        x /= np.linalg.norm(x)
    return np.linalg.norm(A @ x)

ls_pow = power_iteration(A, n_iter=10)
print(ls_pow)