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[Lapack] accuracy and blas

Dear Jonathan,

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 
be well-conditioned.

Routine DGEESX allows you to order the eigenvalues and can compute an 
invariant subspace for the selected eigenvalues.

Best wishes,

Sven Hammarling.

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