The generalized Schur decomposition of an arbitrary pencil A-&lgr;B - robust software with error bounds and applications. Part I: theory and algorithms

@article{Demmel1993TheGS,
  title={The generalized Schur decomposition of an arbitrary pencil A-&lgr;B - robust software with error bounds and applications. Part I: theory and algorithms},
  author={James Demmel and Bo K{\aa}gstr{\"o}m},
  journal={ACM Trans. Math. Softw.},
  year={1993},
  volume={19},
  pages={160-174}
}
Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil A – λB (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of A – λI 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… CONTINUE READING
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