Kostić, Aleksandra; Voss, Heinrich

On Sylvester's law of inertia for nonlinear eigenvalue problems

ETNA, Electron. Trans. Numer. Anal. 40, 82-93, electronic only (2013)


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.

Mathematics Subject Classification

15A18, 65F15


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