Literature Cited
S. K. Godunov, “The problem of dichotomy of the spectrum of a matrix,” Sib. Mat. Zh.,26, No. 5, 25–37 (1986).
S. K. Godunov and A. J. Boulgakov, “Difficultés de calcul dans le problème de Hurwitz et méthodes pour les surmonter,” in: Analysis and Optimization of Systems (Versailles, 1982): Proceedings (Lecture Notes in Control and Information Sciences 44), Springer, Berlin etc. (1982).
A. Ya. Bulgakov and S. K. Godunov, “Computation of positive-definite solutions of Lyapunov's equation,” Trudy Inst. Mat. Akad. Nauk SSSR, Sib. Otd., Vol. 6 (Computational Methods of Linear Algebra), pp. 17–38 (1985).
V. V. Voevodin, “Some methods for solution of the full eigenvalue problem,” Zh. Vychisl. Mat. Mat. Fiz.,2, No. 1, 15–24 (1962).
V. V. Voevodin, “Solution of the full eigenvalue problem by power methods,” in: Computational Methods and Programming [in Russian], Moscow State Univ. (1965), pp. 7–55.
Sh. I. Razzakov, “Qualified estimates of rate of convergence in Voevodin's orthogonal-power method for arbitrary matrices,” Autosibirsk (1983) (Preprint, Akad. Nauk SSSR, Sib. Otd., Vychisl. Tsentr).
Sh. I. Razzakov, “Qualified estimates for rate of convergence in Voevodin's orthogonal-power method for arbitrary matrices,” Author's Abstract of Candidtate's Dissertation, Physical-Mathematical Sciences: 01.01.07, Novosibirsk (1984).
V. I. Kostin and Sh. I. Razzakov, “On the convergence of the orthogonal-power method for computation of the spectrum,” Trudy Inst. Mat. Akad. Nauk SSSR, Sibirskoe Otdelenie, Vol. 6 (Computational Methods of Linear Algebra), pp. 55–84 (1985).
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Dedicated to Sergei L'vovich Sobolev.
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 5, pp. 59–70, September–October, 1988.
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Bulgakov, A.Y., Godunov, S.K. Circular dichotomy of the spectrum of a matrix. Sib Math J 29, 734–744 (1988). https://doi.org/10.1007/BF00970267
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DOI: https://doi.org/10.1007/BF00970267