Spectral Norm by Power Iteration

Problem

Estimate the spectral norm ||A||_2 of matrix A using power iteration on B = A^T A.

Start with v = [1.0, ..., 1.0]. Each iteration computes w = B*v and sets v = w / ||w||_2. After num_iterations, return sqrt(v . (B*v)). Return 0.0 if a normalization step hits the zero vector.

Hint

||A||_2 is the square root of the largest eigenvalue of A^T A.

Test cases

case 1

in: [[[2,0],[0,1]],10]

expected: 1.9999999999993179

case 2

in: [[[1,2],[3,4]],20]

expected: 5.464985704219043

case 3

in: [[[0]],1]

expected: 0

case 4

in: [[[1,0],[0,1]],5]

expected: 1

Starter codePython

def spectral_norm(A, num_iterations):
    # Your code here
    pass

4 test cases · run your code against them in the editor