Geodesic
On Sylvester's law of inertia for nonlinear eigenvalue problems
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 82-93
For Hermitian matrices and generalized definite eigenproblems, the $LDL^H$ factorization provides an easy tool to slice the spectrum into two disjoint intervals. In this note we generalize this method to nonlinear eigenvalue problems allowing for a minmax characterization of (some of) their real eigenvalues. In particular we apply this approach to several classes of quadratic pencils.
Classification : 15A18, 65F15
Keywords: eigenvalue, variational characterization, minmax principle, Sylvester's law of inertia 
@article{ETNA_2013__40__a21,
     author = {Kosti\'c,  Aleksandra and Voss,  Heinrich},
     title = {On {Sylvester's} law of inertia for nonlinear eigenvalue problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {82--93},
     year = {2013},
     volume = {40},
     zbl = {1288.15012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a21/}
}
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AU  - Voss,  Heinrich
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EP  - 93
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%A Voss,  Heinrich
%T On Sylvester's law of inertia for nonlinear eigenvalue problems
%J Electronic transactions on numerical analysis
%D 2013
%P 82-93
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Kostić,  Aleksandra; Voss,  Heinrich. On Sylvester's law of inertia for nonlinear eigenvalue problems. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 82-93. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a21/