GUPTRI software for singular pencils
Reduction to Generalized Upper Triangular (GUPTRI) Form
This page was last updated on 18 May 1999

Contents


Overview

This package of routines contains robust software with error bounds for computing the generalized Schur decomposition of an arbitrary pencil A - zB (regular or singular). The decomposition (GUPTRI - Generalized Upper TRIangular form) is a generalization of the Schur canonical form of A - zI to matrix pencils and reveals the Kronecker structure of a singular pencil.

More information of the package is placed in README, where you also can find references to papers describing software, algorithms and error bounds used in the package. The package is developed by Jim Demmel, University of California, Berkeley, USA and Bo Kågström, Umeå University, Sweden (adresses in README).

Latest version

file linalg/guptri (netlib)
for The GUPTRI package as presented at Netlib.
by Jim Demmel and Bo Kågström
encoding shell archive
gams d4b4
lang Fortran
 
file guptri.tar.gz
for Same as guptri but as a tar/gzip archive.
encoding tar, gzip
 
file mguptri.tar.gz
for Package to make the GUPTRI routine accessible by Matlab. Information on how to use these routines can be found in the included README file.
by Erik Elmroth
encoding tar, gzip
lang Fortran/Matlab

Documentation

This package of routines consists of the following files containing F77 subroutines and functions.

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 programme.
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.

To get more information on how to use GUPTRI in Matlab, enter help guptri after it has been installed correctly.

More information on GUPTRI:
An example in Matlab on how to use GUPTRI.

Contact

Bo Kågström
Department of Computing Science
and High Performance Computer Center North (HPC2N)
Umeå University
SE-901 87 Umeå, Sweden
bokg@cs.umu.se

References

J. Demmel and B. Kågström. 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. Kågström. 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. Kågström. Accurate Solutions of Ill-posed Problems in Control Theory". SIAM J. Matrix Anal. Appl., 9(1):126-145, 1988.

J. Demmel and B. Kågström. Computing Stable Eigendecompositions of Matrix Pencils. Lin. Alg. Appl., 88/89:139-186, 1987.

J. Demmel and B. Kågström. 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, Vol. 127 of North Holland Mathematics Studies, pages 283-323, 1986.

B. Kågström. RGSVD - An Algorithm for Computing the Kronecker Structure and Reducing Subspaces of Singular A - zB Pencils. SIAM J. Sci. Stat. Comp., 7(1):185-211, 1986