@f[
\sum_{{\bf k}, |{\bf k}|\le N}
\longrightarrow
- \sum_{\footnotesize \begin{matrix}{{\bf k}, |{\bf k}|\le N} \\ {|\hat U_{{\bf k}}| \ge |\hat U_{{\bf k}'}|
+ \sum_{\begin{matrix}{{\bf k}, |{\bf k}|\le N} \\ {|\hat U_{{\bf k}}| \ge |\hat U_{{\bf k}'}|
\ \textrm{for all}\ {\bf k}'\ \textrm{with}\ |{\bf k}'|=|{\bf k}|}\end{matrix}}
@f]
This is the form we will implement in the program.
\frac{\eta_{g,K}}{\|\phi_g\|_\infty}
>
\alpha_1
- \displaystyle{\max_{\footnotesize \begin{matrix}1\le g\le G \\ K\in {\cal T}_g\end{matrix}}
+ \displaystyle{\max_{\begin{matrix}1\le g\le G \\ K\in {\cal T}_g\end{matrix}}
\frac{\eta_{g,K}}{\|\phi_g\|_\infty}}
@f}
and coarsen the cells where
\frac{\eta_{g,K}}{\|\phi_g\|_\infty}
<
\alpha_2
- \displaystyle{\max_{\footnotesize \begin{matrix}1\le g\le G \\ K\in {\cal T}_g\end{matrix}}
+ \displaystyle{\max_{\begin{matrix}1\le g\le G \\ K\in {\cal T}_g\end{matrix}}
\frac{\eta_{g,K}}{\|\phi_g\|_\infty}}.
@f}
We chose $\alpha_1=0.3$ and $\alpha_2=0.01$ in the code. Note that this will,
* \relates LinearOperator
*
* Addition of two linear operators @p first_op and @p second_op given
- * by $(\text{first_op}+\text{second_op})x:=\text{first_op}(x)+\text{second_op}(x)$
+ * by $(\text{first\_op}+\text{second\_op})x:=\text{first\_op}(x)+\text{second\_op}(x)$
*
* @ingroup LAOperators
*/
* \relates LinearOperator
*
* Subtraction of two linear operators @p first_op and @p second_op given
- * by $(\text{first_op}-\text{second_op})x:=\text{first_op}(x)-\text{second_op}(x)$
+ * by $(\text{first\_op}-\text{second\_op})x:=\text{first\_op}(x)-\text{second\_op}(x)$
*
* @ingroup LAOperators
*/
* \relates LinearOperator
*
* Concatenation of two linear operators @p first_op and @p second_op given
- * by $(\text{first_op}*\text{second_op})x:=\text{first_op}(\text{second_op}(x))$
+ * by $(\text{first\_op}*\text{second\_op})x:=\text{first\_op}(\text{second\_op}(x))$
*
* @ingroup LAOperators
*/