Commit e9de5627 authored by Daniel Ruprecht's avatar Daniel Ruprecht
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added todo

parent 65670ef7
......@@ -154,7 +154,7 @@ and $ \textbf{Q}_{\Delta,T} = \frac{1}{2}(\textbf{Q}_{\Delta,E}+\textbf{Q}_{\Del
\subsection*{Optimization of Iterationmatrix}
To optimze the SDC iteration we take a look at the properties of our iterationmatrix $\textbf{E}:= \textbf{I} - (\textbf{I}-\textbf{Q}_\Delta \textbf{F})^{-1})(\textbf{I}-\textbf{QF})$. The idea is to minimize either the norm of $\textbf{E}$ or the spectral radius. Therefore we have the two objective functions
To optimze the SDC iteration we take a look at the properties of our iterationmatrix $\textbf{E}:= \textbf{I} - (\textbf{I}-\textbf{Q}_\Delta \textbf{F})^{-1})(\textbf{I}-\textbf{QF})$.\todo{fix brackets?} The idea is to minimize either the norm of $\textbf{E}$ or the spectral radius. Therefore we have the two objective functions
\begin{align}
C_{\mathrm{norm}} (\textbf{E})&= \|\textbf{E}\|_{\infty} \label{eq:costNorm}\\
C_{\mathrm{spec}} (\textbf{E}) &= \rho(\textbf{E})\label{eq:costSpec}.
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