I know that a conjugate gradient method is guaranteed to converge to the solution of a linear system if the matrix is positive definite. I'm working with a family of matrices that have the following properties:
- weakly diagonally dominant
- all nonzero entries are strictly positive.
I don't think these conditions are sufficient to show that the matrix is positive definite, but I still suspect that it will converge. Are there other known conditions under which a system such as this is known to converge?