Example 1 (from Program LA_SBGV_EXAMPLE)

$$A = \left( \begin{array}{rrrrr} 6 & 5 & -4 & 0 & 0\\ 5 &... ... 0 & 2 & 2 & 8 & 3\\ 0 & 0 & 0 & 3 & 10 \end{array} \right)$$

Arrays ${\bf AB}$ and ${\bf BB}$ on entry:

$$\begin{array}{cc} {\bf AB} \\ \begin{array}{\vert rrrrr\v... ...& 3 \\ 10 & 8 & 8 & 8 & 10 \\ \hline \end{array} \end{array}$$

The call:
CALL LA_SBGV( AB, BB, W )

${\bf BB}$ and ${\bf W}$ on exit:

$$\begin{array}{cc} {\bf BB} \\ \begin{array}{\vert lllll\ve... ...es 10^{-1} \\ \;\;\; 1.12617 \\ \hline \end{array} \end{array}$$

The eigenvalues of the problem $A\, z=\lambda \, B\, z$ are:

$$\left( \begin{array}{l} -2.95028 \\ -2.60316 \times 10^{-1... ...341 \times 10^{-1} \\ \;\;\; 1.12617 \\ \end{array} \right).$$

The split Cholesky factor S is:

$$\left( \begin{array}{lllll} 0.00000 & 0.00000 & -1.58114 &... ...& \;\;\; 2.15849 & 2.66458 & 3.16228 \\ \end{array} \right).$$