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Mat. Zametki, 2014, Volume 96, Issue 1, Pages 101–115 (Mi mz9300)  

Hermitian Spectral Pseudoinversion and Its Applications

Yu. M. Nechepurenko

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow

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.

DOI: https://doi.org/10.4213/mzm9300

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English version:
Mathematical Notes, 2014, 96:1, 110–121

Bibliographic databases:

UDC: 519.62
Received: 13.12.2011
Revised: 29.01.2014

Citation: Yu. M. Nechepurenko, “Hermitian Spectral Pseudoinversion and Its Applications”, Mat. Zametki, 96:1 (2014), 101–115; Math. Notes, 96:1 (2014), 110–121

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