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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 ≥ 0a ndA−1 ≤ 0.

Basic comparison theorems for weak and weaker matrix splittings