Geodesic
Structure preserving deflation of infinite eigenvalues in structured pencils
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 1-24
The long standing problem is discussed of how to deflate the part associated with the eigenvalue infinity in a structured matrix pencil using structure preserving unitary transformations. We derive such a deflation procedure and apply this new technique to symmetric, Hermitian or alternating pencils and in a modified form to (anti)-palindromic pencils. We present a detailed error and perturbation analysis of this and other deflation procedures and demonstrate the properties of the new algorithm with several numerical examples.
Classification : 65F15, 15A21, 93B40
Keywords: structured staircase form, structured Kronecker canonical form, symmetric pencil, Hermitian pencil, alternating pencil, palindromic pencil, linear quadratic control, $H_\infty$ control 
@article{ETNA_2015__44__a29,
     author = {Mehrmann,  Volker and Xu,  Hongguo},
     title = {Structure preserving deflation of infinite eigenvalues in structured pencils},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--24},
     year = {2015},
     volume = {44},
     zbl = {1312.65055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a29/}
}
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AU  - Xu,  Hongguo
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%A Xu,  Hongguo
%T Structure preserving deflation of infinite eigenvalues in structured pencils
%J Electronic transactions on numerical analysis
%D 2015
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%F ETNA_2015__44__a29
Mehrmann,  Volker; Xu,  Hongguo. Structure preserving deflation of infinite eigenvalues in structured pencils. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 1-24. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a29/