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TableĀ 2 The different way of rearranging linear systems (4.5) into the form \(x = T(x)\)

From: An inertial parallel algorithm for a finite family of G-nonexpansive mappings with application to the diffusion problem

Linear system Fixed point mapping Tx
\(A \mathbf{u}^{n+1} = \mathbf{G}^{n}\) \(T^{\mathrm{WJ}}\mathbf{u}^{n+1} = ( I - \omega D^{-1} A ) \mathbf{u}^{n} + \omega D^{-1} \mathbf{G}^{n}\)
\(T^{\mathrm{SOR}}\mathbf{u}^{n+1} = ( I - \omega ( D - \omega L )^{-1} A ) \mathbf{u}^{n} + \omega ( D - \omega L )^{-1} \mathbf{G}^{n}\)