Theory and Modern Applications
Table 2 The different way of rearranging linear systems (4.5) into the form \(x = T(x)\)
Linear system | Fixed point mapping Tx |
|---|---|
\(A \mathbf{u}^{n+1} = \mathbf{G}^{n}\) | \(T^{\mathrm{WJ}}\mathbf{u}^{n+1} = ( I - \omega D^{-1} A ) \mathbf{u}^{n} + \omega D^{-1} \mathbf{G}^{n}\) |
\(T^{\mathrm{SOR}}\mathbf{u}^{n+1} = ( I - \omega ( D - \omega L )^{-1} A ) \mathbf{u}^{n} + \omega ( D - \omega L )^{-1} \mathbf{G}^{n}\) |