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Reducing subspaces : definitions, properties and algorithms

Bibliographic reference Van Dooren, Paul. Reducing subspaces : definitions, properties and algorithms. In: B. Kagstrom and A. Ruhe, Matrix Pencils, Springer  1983, p. 58-73
Permanent URL http://hdl.handle.net/2078.1/81214
  1. BOLEY D., Computing the controllability/observability decomposition of a linear time invariant dynamic system, a numerical approach, Ph. D. Thesis, Stanford University, 1981.
  2. Emami-Naeini A., Van Dooren P., Computation of zeros of linear multivariable systems, 10.1016/0005-1098(82)90070-x
  3. Forney, Jr. G. David, Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems, 10.1137/0313029
  4. GANTMACHER F. R., Theory of matrices I & II, Chelsea, New York, 1959.
  5. Moler C. B., Stewart G. W., An Algorithm for Generalized Matrix Eigenvalue Problems, 10.1137/0710024
  6. PAIGE C., Properties of numerical algorithms related to computing controllability, IEEE Trans. Aut. Contr., Vol. AC-26, pp. 130–138.
  7. Stewart G. W., Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems, 10.1137/1015095
  8. Stewart G. W., On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$, 10.1137/0709056
  9. Van Dooren P., The computation of Kronecker's canonical form of a singular pencil, 10.1016/0024-3795(79)90035-1
  10. Van Dooren P., The generalized eigenstructure problem in linear system theory, 10.1109/tac.1981.1102559
  11. Van Dooren P., A Generalized Eigenvalue Approach for Solving Riccati Equations, 10.1137/0902010
  12. WILKINSON J., Linear differential equations and Kronecker's canonical form, Recent Advances in Numerical Analysis, Ed. C. de Boor, G. Golub, Academic Press, New York, 1978.
  13. Wilkinson J.H., Kronecker's canonical form and the QZ algorithm, 10.1016/0024-3795(79)90140-x
  14. Wonham W. Murray, Linear Multivariable Control: a Geometric Approach, ISBN:9781468400700, 10.1007/978-1-4684-0068-7
  15. KUBLANOVSKAYA V., AB algorithm and its modifications for the spectral problem of linear pencils of matrices, LOMI-preprint E-10-81, USSR Academy of Sciences, 1981.
  16. KUBLANOVSKAYA V., On an algorithm for the solution of spectral problems of linear matrix pencils, LOMI-preprint E-1-82, USSR Academy of Sciences, 1982.