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### [Lapack] question about ZHGEQZ for 2x2 block

 ``` Hi Rodney, Thanks to look into the problem. But I am not sure whether the exceptional shift will help. This is the reason why I am asking question for the 2x2 block. Best Regards! Peng HongBo From: "James, Rodney" To: Hong Bo Peng/China/IBM at IBMCN, Cc: "lapack@Domain.Removed" Date: 11/01/2012 07:42 Subject: Re: [Lapack] question about ZHGEQZ for 2x2 block Dear Hong Bo, Thank you for reporting this problem with ZGGEV. I investigated this a bit, and generalized the simple example that demonstrates the problem as follows. Let n=3 and set A to be the identity, and B be the identity with "x" in the first superdiagonal and first subdiagonal elements. The generalized eigenvalue problem for (A,B) has eigenvalues { 1, 1/(1-x), 1/(1+x) }. I tested xGGEV on this real problem for x=10^(-k), with k=1, ..., 20. The real versions (S,D) always converged, but the complex versions (C,Z) failed for a range of values. The single precision complex fails to converge for x= 10^-4, 10^-5, and 10^-6, but converges for values outside that range. The double precision complex fails for a wider range, x = 10^-8 through 10^-15, and converges otherwise. I am not sure why this is happening, but the real and complex versions are somewhat different. In particular, the shift strategies are quite different. It is possible that the exceptional shift used in the complex version just does not work for this test case. Cheers, Rodney On Oct 26, 2012, at 3:55 AM, Hong Bo Peng wrote: ``````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 _______________________________________________ Lapack mailing list Lapack@Domain.Removed http://lists.eecs.utk.edu/mailman/listinfo/lapack `````` -------------- next part -------------- An HTML attachment was scrubbed... URL: http://lists.eecs.utk.edu/mailman/private/lapack/attachments/20121102/29421f45/attachment.html -------------- next part -------------- A non-text attachment was scrubbed... Name: graycol.gif Type: image/gif Size: 105 bytes Desc: not available Url : http://lists.eecs.utk.edu/mailman/private/lapack/attachments/20121102/29421f45/graycol.gif ```
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