Example (from Program LA_SBGVX_EXAMPLE)

The results below are computed with $\epsilon = 1.19209 \times 10^{-7}$.
Matrices $A$ and $B$ are the same as in Example 1 for LA_SBGV.

The call:
CALL LA_SBGVX( A, B, W, Z=Z, VL=0.0_wp, VU=100.0_wp, M=M, Q=Q )^8.2

${\bf W, M}$ and Q on exit:

$$\begin{array}{cc} {\bf W} \\ \begin{array}{\vert rrrrr\ve... ...ray}{c} \\ \begin{array}{c} {\bf M} = 3 \end{array} \end{array}$$

$$\begin{array}{cc} {\bf Q} \\ \begin{array}{\vert crrrr\ver... ...-1} & 6.26144 \times 10^{-2} \\ \hline \end{array} \end{array}$$

The three eigenvalues in the range $[0,100]$ are:

$$\left( \begin{array}{lll} 3.37961 \times 10^{-1} & 8.63341 \times 10^{-1} & 1.12617 \end{array} \right).$$

The matrix $Q$ used in the reduction of $A z = \lambda B z$ to tridiagonal form is:

$$Q = \left( \begin{array}{crrrr} 3.16228 \times 10^{-1} & -1.0... ...\times 10^{-1} & 6.26144 \times 10^{-2} \end{array} \right).$$