F07GTF (ZPPEQU) computes a diagonal scaling matrix
S
chosen so that
This means that the matrix
B
given by
has diagonal elements equal to unity. This in turn means that the condition number of
B
,
κ2B
, is within a factor
n
of the matrix of smallest possible condition number over all possible choices of diagonal scalings (see Corollary 7.6 of
Higham (2002)).
Higham N J (2002)
Accuracy and Stability of Numerical Algorithms (2nd Edition) SIAM, Philadelphia
The computed scale factors will be close to the exact scale factors.
The real analogue of this routine is
F07GFF (DPPEQU).
This example equilibrates the Hermitian positive definite matrix
A
given by
Details of the scaling factors and the scaled matrix are output.