F07FTF (ZPOEQU) computes a diagonal scaling matrix
chosen so that
This means that the matrix
given by
has diagonal elements equal to unity. This in turn means that the condition number of
,
, is within a factor
of the matrix of smallest possible condition number over all possible choices of diagonal scalings (see Corollary 7.6 of
Higham (2002)).
The computed scale factors will be close to the exact scale factors.
The real analogue of this routine is
F07FFF (DPOEQU).
This example equilibrates the Hermitian positive definite matrix
given by
Details of the scaling factors and the scaled matrix are output.