From n=5 on,
there are sufficiently many 4th degree polynomials
to directly solve
linearly.
For the n=5 case, we obtain six 4th degree polynomials, giving the following matrix equation:
If the singular value decomposition of 
is
,
the vector 
is directly obtained as
the right singular vector 
of the smallest singular value
of 
.
Then x can be obtained
using Equation (6),
as for the linear 4-point algorithm.
The same algorithm is also valid
for any 
points.
We just need to SVD the 
matrix
to get the solution for the vector 
.
Hence,
the pose of the calibrated camera is uniquely determined by
point correspondences provided these n points together
with the perspective center
of the camera do not lie in a critical configuration.
The unique solution can be estimated by the linear N-point algorithm.