From: Sven Hammarling
Date: Mon, 04 Jul 2011 12:26:34 +0100
You are not likely to get any improvement in accuracy with the optimized
BLAS. Do you use balancing when calling DGEEVX?
Of course, if the eigenvalues are ill-conditioned that is an inherent
property of the problem and unless your data is very accurate, computing
accurate eigenvalues may not be justified by the data.
Having said that, if you have close eigenvalues, then they are likely to
be ill-conditioned, as are the associated eigenvectors, but if you
consider a subset then the invariant subspace spanned by the subset may
Routine DGEESX allows you to order the eigenvalues and can compute an
invariant subspace for the selected eigenvalues.