SIAM Journal on Scientific and Statistical Computing
Distribution of mathematical software via electronic mail
Communications of the ACM
Accurate solutions of ill-posed problems in control theory
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Computing the controllability - observability decomposition of a linear time-invariant dynamic system, a numerical approach
ACM Transactions on Mathematical Software (TOMS)
A numerically reliable solution for the squaring-down problem in system design
Applied Numerical Mathematics
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
GHM: a generalized Hamiltonian method for passivity test of impedance/admittance descriptor systems
Proceedings of the 2009 International Conference on Computer-Aided Design
MIMO-descriptor systems model reduction
International Journal of Modelling and Simulation
A new approach to modeling multiport systems from fequency-domain data
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An efficient projector-based passivity test for descriptor systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fiedler Companion Linearizations and the Recovery of Minimal Indices
SIAM Journal on Matrix Analysis and Applications
On generalized inverses of singular matrix pencils
International Journal of Applied Mathematics and Computer Science - Semantic Knowledge Engineering
On the Kronecker Canonical Form of Mixed Matrix Pencils
SIAM Journal on Matrix Analysis and Applications
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Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil A – &lgr;B (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of A – &lgr;I to matrix pencils and reveals the Kronecker structure of a singular pencil. Since computing the Kronecker structure of a singular pencil is a potentially ill-posed problem, it is important to be able to compute rigorous and reliable error bounds for the computed features. The error bounds rely on perturbation theory for reducing subspaces and generalized eigenvalues of singular matrix pencils. The first part of this two-part paper presents the theory and algorithms for the decomposition and its error bounds, while the second part describes the computed generalized Schur decomposition and the software, and presents applications and an example of its use.