Abstract:
A description is given of the iterative Jacobi method with overlapping subsystems and the corresponding
Gauss–Seidel method. Similarly to the classical case, a generalized SOR method with overlapping subsystems is constructed by introducing an relaxation parameter. The concept of a $\omega$-consistent matrix is defined. It is shown that, with the optimal choice of the parameter, the theory developed by Young remains valid for $\omega$-consistent matrices. This implies certain results for $\omega$-consistent $H$-matrices. The theoretical conclusions obtained in the paper are supported by numerical results.
Key words:iterative methods for SLAE, generalized SOR method, $H$-matrices.
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