Input:

, and;

step 1:

Compute the eigenvalues and of and, respectively;

Choose an integer such that satisfies the Assumption 1;

step 2:

for do

Compute the;

;;

;

end for

step 3:

for to do

for to do

;

end for

end for

step 4:

;

step 5:

for do

;

end for

Output:

the eigenvalue perturbation bounds;