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Matematicheskie Zametki, 2014, Volume 96, Issue 1, Pages 101–115
DOI: https://doi.org/10.4213/mzm9300 (Mi mzm9300) 		 
Hermitian Spectral Pseudoinversion and Its Applications

Yu. M. Nechepurenko

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/mzm9300
Abstract: The present paper is devoted to the Hermitian spectral pseudoinversion and its applications to analysis, the solution and reduction of Hermitian differential-algebraic systems. New explicit formulas for the solutions of such systems and the solutions of related generalized Lyapunov equations are proposed. Attainable upper bounds for the norms of the solutions are obtained. A realization of the balanced truncation method not requiring computations involving projections onto reducing subspaces is proposed.
Keywords: Hermitian spectral pseudoinversion, Hermitian differential-algebraic system, Lyapunov equation, balanced truncation method, reducing subspace, matrix pencil, initial value problem, controllability Gramian, observability Gramian.
Received: 13.12.2011
Revised: 29.01.2014
English version:
Mathematical Notes, 2014, Volume 96, Issue 1, Pages 110–121
DOI: https://doi.org/10.1134/S0001434614070104
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: Yu. M. Nechepurenko, “Hermitian Spectral Pseudoinversion and Its Applications”, Mat. Zametki, 96:1 (2014), 101–115; Math. Notes, 96:1 (2014), 110–121
Citation in format AMSBIB
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