Till umu.se

GUPTRI software for singular pencils

This package is no longer maintained or supported, and provided "as is".

Overview

This package of Fortran 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. The package is developed by Jim Demmel, University of California, Berkeley, USA and Bo Kågström, Umeå University, Sweden

Download

guptri.tar.gzThe GUPTRI Fortran package.

fguptri.tar.gzPackage to make the GUPTRI routine accessible by Matlab. Information on how to use these routines can be found in the included README file. The MEX files are written for 32-bit versions of Matlab and need to be modified to work on a 64-bit version.

Content

The GUPTRI package of routines consists of the following files containing F77 subroutines and functions. All files start with a statement describing the contents of the actual file.

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














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.

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


Sidansvarig: Frank Drewes

Utskriftsversion

Kontaktinformation

Bo Kågström
Department of Computing Science, Umeå universitet
901 87 Umeå 

Besöksadress
Plan 4, MIT-huset, D453

Tel:  +46 90 7865419

Mobil:  +46 73 6205419

Kontaktformulär

Relaterad information

StratiGraph