I am currently solving a problem that in the process ends up having to solve a linear system. The matrix of this system is not always positive-definite, and at most this matrix can be positive semi-definite.
In the case that the matrix is positive-definite, I use a Cholesky decomposition in the matrix to solve the system. In the other case, I'm using a Conjugated Gradient Least Square algorithm, but I don't know if it's the best way out.
Could you give me suggestions/algorithms for a linear system whose matrix is positive semi-definite?