Geodesic
On Sylvester's law of inertia for nonlinear eigenvalue problems
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 82-93.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {40},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a21/}
}
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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/