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The computation of Kronecker’s canonical form of a singular pencil. (English) Zbl 0416.65026


MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A21 Canonical forms, reductions, classification

Citations:

Zbl 0341.65027
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Full Text: DOI

References:

[1] Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Clarendon: Clarendon Oxford · Zbl 0258.65037
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[10] Jordan, D.; Godbout, L. F., On the computation of the canonical pencil of a linear system, IEEE Trans. Automatic Control, AC-22, 112-114 (Feb. 1977)
[11] Thorp, J. S., The singular pencil of a linear dynamical system, Internat. J. Control, 18, 577-596 (1973) · Zbl 0262.93020
[12] P.Van Doreen and P. Dewilde, State-space realization of a general rational matrix. A numerically stable algorithm, in Proceedings of theMidwest Symposium on Circuits and Systems; P.Van Doreen and P. Dewilde, State-space realization of a general rational matrix. A numerically stable algorithm, in Proceedings of theMidwest Symposium on Circuits and Systems
[13] Morse, A. S., Structural invariants of linear multivariable systems, SIAM J. Control, 11, 446-465 (Aug. 1973)
[14] Rosenbrock, H. H., State-Space and Multivariable Theory (1970), Nelson: Nelson London · Zbl 0246.93010
[15] Kouvaritakis, B., A geometric approach to the inversion of multivariable systems, Internat. J. Control, 24, 609-626 (1976) · Zbl 0336.93002
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[17] Ruhe, A., Algorithms for the nonlinear eigenvalue problem, SIAM J. Numer. Anal., 10, 689-694 (Sept. 1973)
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[20] Van Dooren, P.; Dewilde, P., Polar structure of rational matrices and the realization problem, (Internal Report Div. Appl. Math. Comput. Sci. (1977), K. Univ. Leuven: K. Univ. Leuven Louvain)
[21] Wilkinson, J. H., The differential system Bẋ = Ax and the generalized eigenvalue problem Au = λBu, Nat. Phys. Lab. Report NAC 73 (Jan. 1977)
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