Бибердорф Э.А.  

Development of the dichotomy method of the matrix spectrum and its applications

Development of the dichotomy method of the matrix spectrum and its applications
The dichotomy of the matrix spectrum is a promising alternative to the spectral problem in the classical formulation, especially when applied to the problem of stability. The ideas of the spectral separation with respect to some curves were first algorithmized by  Godunov S.K. and  his co-workers [1]. Attempts to use these methods to study the stability of flows required a whole series of modifications of the existing approaches and the creation of new algorithms [2]. To investigate the stability of near wall flows, an algorithm for the dichotomy of the spectrum of the matrix pencil with respect to  a hyperbola and an analogous parabolic dichotomy algorithm have been developed.
The work was supported by the Russian Foundation for Basic Research (project code 17-01-00791).

Bibliography

  1. Godunov S.K., Sadkane M. Some new algorithms for the spectral dichotomy methods. Linear Algebra Appl. 2003. Vol. 358. P. 173-194.
  2. Biberdorf, E.A., Blinova, M.A. & Popova, N.I. Numer. Analys. Appl. (2018) 11: 108. https://doi.org/10.1134/S1995423918020027


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