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References
S. I. Campbell, C. D. Meyer, and N. J. Rose, “Applications of the Drazin inverse to a linear system of differential equations with singular constant coefficients,” SIAM J. Appl. Math.,31, 411–425 (1976).
Yu. E. Boyarintsev, Regular and Singular Systems of Linear Ordinary Differential Equations [in Russian], Nauka, Novosibirsk (1980).
R. MÄrz, Canonical Projectors for Linear Differential Algebraic Equations [Preprint / Fachbereich Mathematik, Humbold-Univ.; 93–17], Berlin (1993).
S. K. Godunov, A. G. Antonov, O. P. Kirilyuk, and V. I. Kostin, Guaranteed Accuracy in Solving Systems of Linear Equations in Euclidean Spaces [in Russian], Nauka, Novosibirsk (1992).
A. N. Malyshev, Introduction to Computational Linear Algebra [in Russian], Nauka, Novosibirsk (1991).
A. Ya. Bulgakov and S. K. Godunov, “Circular dichotomy of the spectrum of a matrix,” Sibirsk. Mat. Zh.,29, No. 5, 59–70 (1988).
V. N. Kublanovskaya, “On one method for solving the complete eigenvalue problem for a degenerate matrix,” Zh. Vychisl. Matematiki i Mat. Fiziki,6, No. 4, 610–620 (1966).
A. Ruhe, “An algorithm for numerical determination of the structure of a general matrix,” BIT,10, 196–216 (1970).
G. H. Golub and J. Wilkinson, “Ill-conditioned eigensystems and the computation of the Jordan canonical form,” SIAM Rev.,18, 578–619 (1976).
T. Beelen and P. Van Dooren, “Computational aspects of the Jordan canonical form,” in: Reliable Numerical Computation, Oxford Univ. Press, New York, 1990, pp. 57–72.
F. R. Gantmakher, The Theory of Matrices [in Russian], Nauka, Moscow (1988).
C. L. Lawson and R. J. Hanson, Solving Least Squares Problems [Russian translation], Nauka, Moscow (1986).
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Translated fromSibirskii Matemaiicheskii Zhurnal, Vol. 36, No. 5, pp. 1194–1207, September–October, 1995.
In conclusion, the author expresses her gratitude to V. I. Kostin for help and sound advice, to S. K. Godunov for the observation that resulted in the structure of § 1 of the present article and led to appearance of the systems of equations (2), (9), and to the referee who drew the author's attention to the interesting articles [9, 10].
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Shtykel', T.L. To the theory of degenerate systems of ordinary differential equations. Sib Math J 36, 1035–1047 (1995). https://doi.org/10.1007/BF02112544
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DOI: https://doi.org/10.1007/BF02112544