A linear equation system 
, with 
being an 
matrix and 
, is called an overdetermined linear system. In general, it has no classical solution and you seek a vector 
with the property:
Here, 
denotes the Euclidean vector norm 
.
This problem is called a least square problem. A stable method to solve it is based on factorizing 
, with 
being an 
orthogonal matrix, 
an 
orthogonal matrix, and 
an 
matrix with the property 
for all 
. This factorization is called a singular value decomposition (SVD).
We write
with a diagonal 
matrix 
. If we assume that 
has full rank, then 
is invertible and it can be shown that
holds.
If we split 
with 
being an 
submatrix, then the preceding equation can be simplified to:
SciPy provides a function called svd, which we use to solve this task:
import scipy.linalg...