5.8 Preconditioning of iterative methods

Expressing the type conversion  $\underline{{\ensuremath{\color{red}\mathfrak{w}}}} = \sum_{j=1}^{P} A_j^T \underline{{\ensuremath{\color{green}{\sf r}}}}_j$ in the CG (Alg. 5.2) as a matrix results in the type-I (accumulated) identity and is equivalent to (4.11b) with the components ${\ensuremath{\color{red}\mathfrak{M}}}_D = {\ensuremath{\color{red}\mathfrak{I}}}$ and ${\ensuremath{\color{red}\mathfrak{M}}}_L = {\ensuremath{\color{red}\mathfrak{M}}}_U = 0$. Therefore, we are looking for preconditioners not requiring essentially more communication then this type conversion.