Basic comparison theorems for weak and weaker matrix splittings

The main goal of this paper is to present comparison theorems proven under natural conditions such as N2 ≥ N1 and M−1 1 ≥ M−1 2 for weak and weaker splittings of A = M1 − N1 = M2 − N2 in the cases when A−1 ≥ 0 and A−1 ≤ 0.