This package of routines for computing the generalized Schur decomposition
of an arbitrary (singular) pencil A-zB consists of the following files
containing F77 subroutines and functions belonging to this package.
They are:
	zblas.f
	zbnd.f             subroutines bound and evalbd described in software paper
	zcmatmlr.f
	zguptri.f          subroutine guptri described in software paper
	zlinpack.f
	zlistr.f
	zmiscl.f
	zqz.f
	zrcsvdc.f
	zreorder.f         subroutine reordr described in software paper
	zrzstr.f

All these files start with a statement describing the contents of
the actual file.


Enclosed with these files are also 
	zgschurm.f   example program 
	kcfin.c1     input file for zgschurm.f for example C1 in software paper
	zgschur.c1   output file for example C1 in paper


A standard usage of the package is as follows:

  call guptri (...) Compute generalized Schur decomposition of singular A-zB.
  call reordr (...) Reorder the eigenvalues in specified order.
  call bound  (...) Compute error bounds for selected eigenvalues
  call evalbd (...) and reducing subspaces.

The following papers describe software,algorithms and error bounds
used in the package:
J. Demmel and B. Kagstrom. "The generalized Schur decomposition 
   of an arbitrary pencil A - zB: robust software with error bounds 
   and applications. Part I: theory and algorithms.". ACM Trans. 
   Math. Softw., 19(2):160-174, 1993

J. Demmel and B. Kagstrom. "The generalized Schur decomposition of 
   an arbitrary pencil A - zB: robust software with error bounds 
   and applications. Part II: software and applications." ACM Trans. 
   Math. Softw., 19(2):175-201, 1993

J. Demmel and B. Kagstrom, "Accurate Solutions of Ill-posed Problems
   in Control Theory", SIAM J. Matrix Anal Appl, Vol 9, 1988, pp 126-145

J. Demmel and B. Kagstrom, "Stable Eigendecompositions of Matrix Pencils",
   Linear Algebra Applic., Vol 88/89, 1987, pp 137-186

J. Demmel and B. Kagstrom, "Stably Computing the Kronecker Structure
   and Reducing Subspaces of Singular pencils A-zB for Uncertain Data",
   in J. Cullum and R. Willoughby (eds), Large Scale Eigenvalue Problems,
   North Holland, 1986, pp 283-323

B. Kagstrom, "RGSVD - An Algorithm for Computing the Kronecker Structure
   and Reducing Subspaces of Singular Matrix Pencils", SIAM J. Sci. Stat.
   Comp., Vol 7, 1986, pp 185-211

Any comments or questions should be sent to:

	Bo Kagstrom
	Department of Computing Science and
        High Performance Computing Center North (HPC2N)
	Umea University
	S-901 87 Umea, Sweden
	email: bokg@cs.umu.se

	or

	James Demmel
	University of California
        Division of Computer Science
        737 Soda Hall
        Berkeley CA 94720
	email: demmel@cs.berkeley.edu

Notices:
1. The main program in file zgschurm.f with input from kcfin.c1
   produced the output on file zgschur.c1 when run on
   Sun 3/80 workstation. The output in file zgschur.c1 also
   includes some information that is not explained in the software paper.
   We refer to the source for more information.  

2. The current version of the package has been developed during a period
   of 4-5 years. The current version of the routines does not make use
   of level 2 or 3 BLAS.

3. Before a production code of this package is produced we would like
   to obtain and collect as much information from users as possible.
   THANK YOU IN ADVANCE!