On exit: for CG and SYMMLQ methods, the current estimate of the largest singular value
${\sigma}_{1}\left(\overline{A}\right)$ of the preconditioned iteration matrix
$\overline{A}={E}^{-1}A{E}^{-\mathrm{T}}$, when either it has been supplied to
f11gdc or it has been estimated by
f11gec (see also
Sections 3 and
5 in
f11gdc). Note that if
${\mathbf{its}}<{\mathbf{itn}}$ then
sigmax contains the final estimate. If, on final exit from
f11gec,
${\mathbf{its}}={\mathbf{itn}}$, the estimation of
${\sigma}_{1}\left(\overline{A}\right)$ may have not converged; in this case you should look at the value returned in
sigerr. Otherwise,
${\mathbf{sigmax}}=0.0$ is returned.
For MINRES method, an estimate of the final transformed residual.