Some publications of the subproject:

Perturbation Analysis, Condition Estimation
and Reliable Error Bounds

The listings of publications are in reversed chronological order.

Submitted papers and work in progress

Refereed journal publications and invited book chapters

• Parallel Solvers for Sylvester-type Matrix Equations with Applications in Condition Estimation, Part I: Theory and Algorithms, Robert Granat and Bo Kågström, ACM Trans. Math. Software (accepted), Feb. 2010. (pdf)
   
• AlGORITHM XXX. The SCASY Software Library, Parallel Solvers for Sylvester-type Matrix Equations with Applications in Condition Estimation, Part II, Robert Granat and Bo Kågström, ACM Trans. Math. Software (accepted), Feb. 2010. (pdf)
   
• Stratification of Controllability and Observability Pairs - Theory and Use in Applications, Erik Elmroth, Stefan Johansson, and Bo Kågström. SIAM J. Matrix Analysis and Applications, Vol. 31, Issue 2, pp. 203-226 (2009) (pdf)
   
• On the structured distance to uncontrollability, M. Karow and D. Kressner, Systems Control Lett., 58(2):128-132, 2009. (pdf)
   
• Structured Hölder condition numbers for multiple eigenvalues, Daniel Kressner, Maria J. Peláez, and J. Moro, SIAM J. Matrix Anal. Appl., 31(1):175-201, 2009. (Also as Report UMINF-06.xx). (pdf)
   
• The effect of aggressive early deflation on the convergence of the QR algorithm, Daniel Kressner, SIAM J. Matrix Anal. Appl.30(2):805-821, 2008. (Also as Report UMINF-06.xx). (pdf)
   
• Structured condition numbers for invariant subspaces, Ralph Byers and Daniel Kressner, SIAM J. Matrix Anal. Appl., 28(2):326-347, 2006. (pdf)
   
• On the sensitivity of the spectral projection, Ji-guang Sun, Linear Algebra Appl., 395 (2005), 83-94. (pdf)
   
• Perturbation bounds for subspaces associated with periodic eigenproblems, Ji-guang Sun, Taiwanese Journal of Mathematics, 9, No.1, 17-38 (2005) . (pdf)
   
• A note on backward errors for structured linear systems, Ji-guang Sun, Numer.Linear Algebra Appl, 12, 585-603 (2005) (pdf)
   
• Backward perturbation analysis of the periodic discrete-time algebraic Riccati equation, Ji-guang Sun, SIAM J. Matrix Anal. Appl., 26 (2004), 1-19. (pdf)
   
• Structured backward error for the linear system $A^TAx=b$, Ji-guang Sun, Journal of Natural Sciences of Heilongjiang University, 21, No.4 (2004), 4-10. (pdf)
   
• Bounds for the Distance Between Nearby Jordan and Kronecker Structures in a Closure Hierarchy, Erik Elmroth, Pedher Johansson, and Bo Kågström, Journal of Mathematical Sciences, Vol, 112, No. 6, 2003, pp. 1765-1779. (pdf)
   
• Perturbation analysis of the matrix equation $X=Q+A^H(\hat{X}-C)^{-1}A$, Ji-guang Sun, Linear Algebra Appl., 372 (2003), 33--51. (pdf)
  

Refereed conference proceedings

• Orbit and bundle stratification for controllability and observability matrix pairs in StratiGraph, Erik Elmroth, Pedher Johansson, Stefan Johansson, and  Bo Kågström, Mathematical Theory of Networks and Systems, MTNS2004, Katholieke Universiteit Leuven, July, 2004. (10 pages, pdf).
   

Technical reports and other publications

• Reviewing the Closure Hierarchy of Orbits and Bundles of System Pencils and Their Canonical Forms, Stefan Johansson, Report UMINF 09.02,, Dept. of Computing Science, Umeå University, Sweden, 2009. (pdf)
   
• Matrix Canonical Structure Toolbox, Pedher Johansson, Report UMINF 06.15, Dept. of Computing Science, Umeå University, Sweden, 2006. (pdf)
   
• On the sensitivity of the oblique projection, Ji-guang Sun, Report UMINF 05.03, ISSN-0348-0542, Dept. of Computing Science, Umeå University, S-901 87 Umeå, Sweden, 2005. (pdf)
   
• A note on perturbation expansions for small singular values, Ji-guang Sun, Report UMINF 03.07, Dept. of Computing Science, Umeå University, S-901 87 Umeå, Sweden, 2003. (pdf)
   
• Condition numbers of spectral projections, Ji-guang Sun, Report UMINF 02.18, Dept. of Computing Science, Umeå University, S-901 87 Umeå, Sweden, 2002. (pdf)

Theses

• Algorithms and Library Software for Periodic and Parallel Eigenvalue Reordering and Sylvester-Type Matrix Equations with Condition Estimation, Robert Granat, PhD Thesis, UMINF 07.21, Dept. of Computing Science, Umeå University, Sweden, ISBN 978-91-7264-410-6, November 2007. (pdf)
  
• Stratification of Matrix Pencils in Systems and Control: Theory and Algorithms, Stefan Johansson, Ph Licentiate Thesis, UMINF 05.17, Dept. of Computing Science, Umeå University, Sweden, ISBN 91-7305-901-3, May 2005. (pdf)