Geodesic
Hermitian Spectral Pseudoinversion and Its Applications
Matematičeskie zametki, Tome 96 (2014) no. 1, pp. 101-115

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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. 
@article{MZM_2014_96_1_a8,
     author = {Yu. M. Nechepurenko},
     title = {Hermitian {Spectral} {Pseudoinversion} and {Its} {Applications}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {101--115},
     publisher = {mathdoc},
     volume = {96},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a8/}
}
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Yu. M. Nechepurenko. Hermitian Spectral Pseudoinversion and Its Applications. Matematičeskie zametki, Tome 96 (2014) no. 1, pp. 101-115. http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a8/