I currently working on a 3d physics engine solver. The result from my collision detection is a set of contact points. A contact point consist of a point, a normal vector and two tangent vectors (for friction). I create a coefficient matrix for the entire system of bodies by splitting each contact point into 3 rows, one for the normal and one for each tangent. Any force interacting with a body will get non-zero values in the coefficient matrix for any constraint row on that body.
I created a general Jacobi iterative matrix solver to solve this linear system, but as my unit tests prove, certain matrices will not converge even though they have valid solutions. I researched online and learned that the Jacobi method is only guaranteed to converge when the coefficient matrix is diagonally dominant.
So my question is this: Is the coefficient matrix guaranteed to be diagonally dominant when generated from contact points?