Inverse Power Method Step

Problem

Perform one inverse power iteration step on the 2x2 matrix A with shift mu and vector v:

Solve (A - mu*I) * y = v, then return the unit vector y / ||y||_2.

Return None if (A - mu*I) is singular.

Hint

The inverse iteration converges to the eigenvector of the eigenvalue closest to mu.

case 1

in: [[[2,0],[0,3]],1.9,[1,0]]

expected: [1,0]

case 2

in: [[[2,0],[0,3]],1.9,[1,1]]

expected: [0.9958932064677037,0.09053574604251859]

case 3

in: [[[3,1],[1,3]],1.5,[1,1]]

expected: [0.7071067811865475,0.7071067811865475]

case 4

in: [[[2,0],[0,3]],2,[1,0]]

expected: null

Starter codePython

def inverse_power_step(A, mu, v):
    # Your code here
    pass

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