Example 1

The band storage scheme is illustrated by the following example, where $n=9$, $kl = 2$ and $ku = 1$, making $size({\bf AB},1) = 6$ and $size({\bf AB},2) = 9$.

$$A = \left( \begin{array}{rrrrrrrrr} a_{11} & a_{12} \\ a_{... ...\\ & & & & & & a_{97} & a_{98} & a_{99} \end{array} \right)$$

$$\begin{array}{c} \mbox{\bf AB} \;\; \mbox{on entry} \end{array}$$

$$\begin{array}{\vert ccccccccc\vert} \hline \ast & \ast & \a... ...} &a_{75} &a_{86} &a_{97} & \ast & \ast \\ \hline \end{array}$$

$$\begin{array}{c} \mbox{\bf AB} \;\; \mbox{on exit} \end{array}$$

$$\begin{array}{\vert ccccccccc\vert} \hline \par\ast & \ast &... ... }&m_{75}& m_{86 }&u_{97 }& \ast & \ast \\ \hline \end{array}$$

Elements marked $\ast$ are not referenced by the routine. Elements marked $\circ$ need not be set on entry. This extra space is needed for $U$ because of the row interchanges.