Theory and Modern Applications
Table 3 Implemented weight parameter and optimal weight parameter of operator S
The different types of operator S | Implement weight parameter ω | Optimal weight parameter \(\omega _{o}\) |
|---|---|---|
\(S^{\mathrm{WJ}} \) | \(0 < \omega < 2\min \{ \frac{\lambda _{\min }(D)}{\lambda _{\min }(A)}, \frac{\lambda _{\max }(D)}{\lambda _{\max }(A)} \} \) | \(\omega _{o} =\frac{1}{2} ( \lambda _{\min }(A) + \lambda _{\max }(A) )\) |
\(S^{\mathrm{SOR}}\) | 0<ω<2 | \(\omega _{o} = \frac{2d}{d + \sqrt{\lambda _{\min }(A) \lambda _{\max }(A)}}\) |