`GUPTRI software for singular pencils`

Reduction to Generalized Upper Triangular (GUPTRI) Form

This page was last updated on 18 May 1999

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).

`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` |

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.

Department of Computing Science

and High Performance Computer Center North (HPC2N)

Umeå University

SE-901 87 Umeå, Sweden

bokg@cs.umu.se

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