Algorithm 4 Eigenpair Computation using Newton’s method in complex arithmetic [7]
Input: 
and tol.
1: for 
until convergence do
2: Compute the LU factorisation of 
3: Form 
4: Solve the lower triangular system 
for
.
5: Solve the upper triangular system 
for
.
6: Update 
7: end for
Out for:
.