The method of normal equation consists in solving
The solution is:
The matrix is SPD. So the system can be solved using Cholesky.
This method is best for very tall skinny .
One of the main drawbacks is that the condition number grows very quickly! Indeed we can prove that
So the condition number grows much faster than .
This method requires to be non-singular. This is equivalent to saying that should be full column rank.
The computational cost is .
Least-squares problems, Symmetric Positive Definite Matrices, Cholesky factorization, Conditioning of a linear system, Stability of the Cholesky factorization