Lower bound for the convergence rate of nonstationary Jacobi-like iteration

Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix $A$ is an $H$-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with $\langle A\rangle$ as the coefficient matrix, where $\langle A\rangle$ is a comparison matrix of $A$.