structural:scholar_edition
Convergence

The choice of relaxation factor ω is not necessarily easy, and depends upon the properties of the coefficient matrix. In 1947, Ostrowski proved that if A {\displaystyle A} is symmetric and positive-definite then ρ (L ω) < 1 {\displaystyle \rho (L_{\omega })<1} for 0 < ω < 2 {\displaystyle 0<\omega <2}. Thus, convergence of the iteration process follows, but we are generally interested in faster convergence rather than just convergence.