Condition Estimate via Power Iterations

Problem

Estimate the 2-norm condition number of A as the ratio sigma_max / sigma_min.

Use power iteration (starting from all ones) on B = A^T A to get sigma_max, and on inv(B) to get 1 / sigma_min; return their product. Return None if B is singular.

Hint

The largest eigenvalue of inv(A^T A) is the reciprocal of the smallest eigenvalue of A^T A.

Test cases

case 1

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

expected: 2

case 2

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

expected: 1

case 3

in: [[[1,2],[3,4]],30]

expected: 14.933034373659252

case 4

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

expected: 1.9387489019317519

Starter codePython

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

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