  The paper presents a comparative analysis of iterative numerical methods of
Jacobi and Gauss-Seidel for solving systems of linear algebraic equations
(SLAEs) with complex and real matrices. The ranges of convergence for both
methods for SLAEs in two and three unknowns, as well as the interrelationships
of these ranges are obtained. An algorithm for determining the convergence of
methods for SLAEs using the complex analog of the Hurwitz criterion is
constructed, the realization of this algorithm in Python in the case of SLAEs
in three unknowns is given. A statistical comparison of the convergence of both
methods for SLAEs with a real matrices and the number of unknowns from two to
five is carried out.
