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Ufimsk. Mat. Zh., 2009, Volume 1, Issue 4, Pages 125–132 (Mi ufa36)  

This article is cited in 2 scientific papers (total in 2 papers)

Upper bounds for the solution norms of the Hermitian ODAE systems

Yu. M. Nechepurenkoa, G. V. Ovchinnikovb

a Institute of Numerical Mathematics, Russian Academy of Sciences
b Moscow Institute of Physics and Technology

Abstract: New reachable bounds for the solution norms of the Hermitian systems of ordinary differential and algebraic equations (ODAEs) are proposed and justified. Matrices possessing properties similar to those of pseudo-inverse ones are defined based on the Cauchy integral theorem. These matrices are used to obtain systems of ODEs corresponding to the finite eigenvalues of the original systems. We show that the proposed upper bounds can be computed with known numerical algorithms and compare them with ones based on the Lyapunov equations.

Keywords: systems of ordinary differential and algebraic equations, initial value problems, reachable upper bounds, pseudo-inverse matrices, spectral projectors, Lyapunov equations.

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Bibliographic databases:
UDC: 519.61
Received: 28.10.2009

Citation: Yu. M. Nechepurenko, G. V. Ovchinnikov, “Upper bounds for the solution norms of the Hermitian ODAE systems”, Ufimsk. Mat. Zh., 1:4 (2009), 125–132

Citation in format AMSBIB
\Bibitem{NecOvc09}
\by Yu.~M.~Nechepurenko, G.~V.~Ovchinnikov
\paper Upper bounds for the solution norms of the Hermitian ODAE systems
\jour Ufimsk. Mat. Zh.
\yr 2009
\vol 1
\issue 4
\pages 125--132
\mathnet{http://mi.mathnet.ru/ufa36}
\zmath{https://zbmath.org/?q=an:1240.34019}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. M. Nechepurenko, “Hermitian Spectral Pseudoinversion and Its Applications”, Math. Notes, 96:1 (2014), 110–121  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Yu. M. Nechepurenko, G. V. Ovchinnikov, M. Sadkane, “Application of the spectral pseudo-inversion to solving Hermitian systems of differential–algebraic equations”, J. Comput. Appl. Math., 260 (2014), 218–228  crossref  mathscinet  zmath  isi  elib  scopus
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