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[Lapack] question about ZHGEQZ for 2x2 block

Hej Peng,

The 2x2 blocks should only appear in real arithmetic (S/D) and then
they correspond to complex conjugate pairs of eigenvalues for
real matrix pairs (A, B). The complex generalized Schur form (C/Z) should
be upper triangular and you can read of the eigenvalues from the pairs
(s_ii, t_ii) where s_ii and t-ii are diagonal entries (complex numbers) of
the generalized Schur form S - sT  (= Q^T (A-sB) Z ).

What type of code are you developing and for what architecture(s)?
How big are the problems you are trying to solve?

Best wishes,
Bo K?gstr?m

Hi,

I am working on GGEV code. But I found ZGGEV failed to converge in one 
sample. I found it is similar to what has been reported in this 
mailing-list. Do we have any update for this problem?
_http://icl.cs.utk.edu/lapack-forum/archives/lapack/msg00535.html_

With more debug print output, I think ZHGEQZ failed to converge 
because it can't get eigenvalue for the 2x2 block. There is a 
difference between DHGEQZ and ZHGEQZ.  DHGEQZ has special code to 
handle the 2x2 block but ZHGEQZ doesn't. Is there any special 
consideration about this in C/ZHGEQZ? As what I found in debug output, 
the implicit sweep doesn't change the 2x2 block (H is 2x2 and T is 2x2 
upper triangular) even with exceptional shift. So it failed to converge.

Best Regards!
Peng HongBo


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