# why there is no relaxation method for Jacobi linear system iterative methods?

I found that the relaxation methods for solving linear system as an iterative sequence are derived from the Gauss-Seidel method and not from the Jacobi method. I understand that the Gauss-Seidel method might look better behaved and in many cases have a smaller spectral radius than that of the Jacobi method. However, once we introduce a relaxation parameter $$\omega$$, things might change. Or, if they do not improve can anyone show why doing a Jacobi-based relaxation would be a bad idea? That is $$$$\bf{x}_{k+1} = (\rm 1 - \omega) \bf{x}_k + \omega \, Jacobi\_Iteration( \bf{x}_k).$$$$ does not converge faster in any situation that $$$$\bf{x}_{k+1} = (\rm 1 - \omega) \bf{x}_k + \omega \, Gauss\_Seidel\_Iteration( \bf{x}_k) ?$$$$

Thanks.