Volume 40, pp. 82-93, 2013.

On Sylvester's law of inertia for nonlinear eigenvalue problems

Aleksandra Kostić and Heinrich Voss

Dedicated to Lothar Reichel on the occasion of his 60th birthday

Abstract

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.

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Key words

eigenvalue, variational characterization, minmax principle, Sylvester's law of inertia

AMS subject classifications

15A18, 65F15

Links to the cited ETNA articles

[18]	Vol. 36 (2009-2010), pp. 113-125 Markus Stammberger and Heinrich Voss: On an unsymmetric eigenvalue problem governing free vibrations of fluid-solid structures

ETNA articles which cite this article

Vol. 55 (2022), pp. 1-75 Jörg Lampe and Heinrich Voss: A survey on variational characterizations for nonlinear eigenvalue problems