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QZ algorithm

• To: mathgroup at smc.vnet.net
• Subject: [mg25016] QZ algorithm
• From: "Luther Flippen" <lflippen at arl.army.mil>
• Date: Fri, 1 Sep 2000 01:09:50 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

To whomever can help me:

I have a question which I originally posed to Mathematica support (see
below). Essentially, I would like to compute generalized
eigenvalues/eigenvectors for a matrix pencil (pair of matrices) without a
priori constraints upon the matrices (such as positive definiteness). The
QZ algorithm is the standard one for this, but I cannot find it for use in
Mathematica and I would prefer not to have to program it myself (even
though I could use Golub's book to do so). This algorithm has an
implementation in LAPACK in Fortran, but I would then have to invest in a
compiler for Windows NT and link it to Mathematica with MathLink (with
which I have little experience).

Posed to Mathematica support:
Question or Problem:
Mathematica has the functions for obtaining eigenvalues/eigenvectors of
individual matrices, but I would like to be able to compute generalized
eigenvalues/eigenvectors for matrix pencils (pairs of matrices) WITHOUT
any special requirements such as positive definiteness. The standard
algorithm for this is the QZ algorithm described in Golub's book on matrix
methods. How can I access this capability within Mathematica without
having to program it from scratch myself. (A built-in version would be far
more efficient than anything I could program in Mathematica anyway.)

They suggested that I try mathgroup.

Dan Flippen

- Dr. L. D. Flippen, Jr. (Dan)        US Army Research Lab
  Sensor Integration Branch           ATTN:  AMSRL-SE-SS
  phone: 301-394-1003                 2800 Powder Mill Road
  fax:   301-394-4605                 Adelphi, MD 20783-1197
  email: lflippen at arl.army.mil
  Bldg. 204, Room 3C094