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Example 1 (from Program LA_HPGV_EXAMPLE)


\begin{displaymath}
A = \left( \begin{array}{lllll}
0 & \;\;\;9 -2i & \;\;\;5 ...
...\;7 +\;\:i& -4 - \;\:i & -11 & \;\;\;\;9
\end{array} \right),
\end{displaymath}


\begin{displaymath}
B = \left( \begin{array}{lllll}
\;\;\;10 & -\;1 -4i & -\;2...
...& \;\;\;\;1 & -\;1 & -\;1+\;\:i & \;\;\;11
\end{array} \right)
\end{displaymath}

Arrays ${\bf AP}$ and ${\bf BP}$ on entry:

\begin{displaymath}
\begin{array}{cc} {\bf AP} \\
\begin{array}{\vert ccccccc...
...,0) &
(3,-1) &
(-9,-1) \\
\hline \end{array} \end{array}
\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf AP\ continued} \\
\begin{array}{cc...
... (-4,1) &
(-11,0) &
(9,0) \\
\hline \end{array} \end{array}\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf BP} \\
\begin{array}{\vert ccccccc...
...10,0) &
(-6,4) &
(0,1) \\
\hline \end{array} \end{array}
\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf BP\ continued} \\
\begin{array}{cc...
...-1,0) &
(-1,-1) &
(11,0) \\
\hline \end{array} \end{array}\end{displaymath}

The call:
CALL LA_HPGV( AP, BP, W )

BP and W on exit:


\begin{displaymath}
\begin{array}{cc} {\bf BP} \\
\begin{array}{\vert ccc} \h...
...26491) &
(3.04959,0.00000) \\
\hline \end{array} \end{array}\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf BP\ continued} \\
\begin{array}{c@{\...
...^{-1}) &
(2.90532,0.00000) \\
\hline \end{array} \end{array}\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf BP\ continued} \\
\begin{array}{ccc}...
...675,-1.36939 \times 10^{-1}) \\
\hline \end{array} \end{array}\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf BP\ continued} \\
\begin{array}{ccc}...
...{-1},1.63957 \times 10^{-1}) \\
\hline \end{array} \end{array}\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf BP\ continued} \\
\begin{array}{ccc\...
...^{-1}) &
(2.80072,0.00000) \\
\hline \end{array} \end{array}\end{displaymath}


\begin{displaymath}
\begin{array}{cc} {\bf W} \\
\begin{array}{\vert l\vert} ...
...\; 1.56312 \\ \;\;\; 16.6680 \\
\hline \end{array} \end{array}\end{displaymath}

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

\begin{displaymath}\left( \begin{array}{l}
-1.02534 \\ -4.96729 \times 10^{-1} ...
...{-1} \\ \;\;\; 1.56312 \\ \;\;\; 16.6680
\end{array} \right). \end{displaymath}

The triangular factor $U$ of the Cholesky factorization of $B$ is:

\begin{displaymath}
U = \left(
\begin{array}{lll}
3.16228 & -3.16228 \times 10^{...
...0.00000 & \;\;\: 0.00000 & \;\;\: 0.00000
\end{array} \right.
\end{displaymath}


\begin{displaymath}
\left.
\begin{array}{ll}
-1.89737 \hspace{1.17 cm} + 1.26491...
...{-1}i \\
\;\;\: 0.00000 & \;\;\: 2.80072
\end{array} \right).
\end{displaymath}


next up previous contents index
Next: Example 2 (from Program Up: Examples Previous: Examples   Contents   Index
Susan Blackford 2001-08-19