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[Lapack] accuracy and blas

I apologise in advance that this is a rather ill-informed question: 
numerical linear algebra is not my field, and I got conflicting advice 
from my numerical analysis colleagues when I asked them about this.....
I am using DGEEVX to calculate eigenvalues/eigenvectors of some real 
non-symmetric matrices (typical size 1000x1000). The matrices have a 
large condition number and the lapack-estimated errors bounds EERRBD are 
quite significant for the eigenvalues close to the origin. Currently I 
am just using the generic blas routines. I realise that using an 
optimized blas library would speed up the calculations, though that is 
not a big issue for me. But I am wondering whether I would be likely to 
get any reduction in errors by using an optimized blas?
Thanks very much
Jonathan Sherratt
Professor of Mathematics
Heriot-Watt University
Edinburgh, UK

Heriot-Watt University is a Scottish charity
registered under charity number SC000278.

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