4.3.3.4 Matrix-by-Vector multiplication.

Contrary to Sec. 4.3.1, the Matrix-by-Vector multiplication $\underline{{\ensuremath{\color{red}\mathfrak{w}}}} = \widetilde{{\ensuremath... ...athfrak{K}}}} \makebox[0pt]{}\underline{{\ensuremath{\color{red}\mathfrak{u}}}}$ is admissible with the type-I vectors $\underline{{\ensuremath{\color{red}\mathfrak{w}}}}$ and  $\underline{{\ensuremath{\color{red}\mathfrak{u}}}}$. The reason is, that we have to store the components of the most outer layer of nodes in  $\underline{{\ensuremath{\color{red}\mathfrak{u}}}}$ but not in  $\underline{{\ensuremath{\color{red}\mathfrak{w}}}}$. If one needs (in a later step of the algorithm) also those boundary components of  $\underline{{\ensuremath{\color{red}\mathfrak{w}}}}$, then an additional communication is required.