From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: URGENT algorithm for the generalized Schur decomposition (QZ)
Date: 3 Jan 2000 17:38:32 GMT
Newsgroups: sci.math.num-analysis
Summary: [missing]

In article <386695B5.B8D6F98B@club-internet.fr>,
 Dominique ALLAIN <domalla@club-internet.fr> writes:
|> If we have A,B square matrices, then there exist unitary matrices such
|> that QAZ and QBZ are upper triangular.
|> 
|> I can't find an algorithm which could give me these two matrices !!!
|> 
|> Thanks a lot for your help
|> 
|> Guillaume
|> 
you mean the QZ algorithm of Stewart and Moler. This is described in the
book
Golub, G.H., van Loan, Ch.:Matrix computations. 3rd ed. 1996. John Hopkins
press.
It goes in two stages. The first stage is finite and reduces A to upper
Hessenberg and B to upper triangular form with a technique similar to the 
Householder QR decomposition. the next stage is iterative and a generalization
of the QR algorithm for the ordinary eigenvalue problem. there is no closed
(finite) algorithm of course.
hope that helps
peter