Abstract
In this paper a number of theorems and lemmas are stated and proved, which can be used as criteria for the evaluation of some unknown eigenvalues of the coefficient matrix of a complex linear system in connection with a consistent with the linear system stationary iterative scheme. The aforementioned eigenvalues can be used together with or without the iterative approximations to improve the convergence rates of the iterative scheme. Numerical examples show the validity of the theory developed.
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