In my recent exercise, I were to write a function that get a matrix A and a number k, and gives the k-th approximation to A's eigenvalues, using the approximation formulas of Rayleigh Quotient Iteration. I wrote the following function, made sure the first iteration is okay, but then the second get as error, and I don't know how to maintain a matrix or a vector the way there are. I am frustrated and would really appreciate any kind of help.
def RayleighQuotientItreation(A,k):
import math
import numpy as np
I=np.matrix(np.identity(A.shape[0]))
b=np.random.rand(A.shape[0])
b=math.pow(normal(b),-1)*b
u=(np.dot(b,(np.dot(A.T,b)).T))[0,0]
for i in range(0,k):
b, u=(np.dot(np.linalg.inv((A- u*I)).T,b))*math.pow(normal((np.dot(np.linalg.inv((A-u*I)),b)).T),-1), (np.dot((np.dot(b.T,A)),b))[0,0]
return u