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arXiv · 2601.15789

Localization of complementarity eigenvalues

Antonio Sasaki·Sophie Demassey·Valentina Sessa
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Abstract

Let A, B be symmetric n x n real matrices with B positive definite and strictly diagonally dominant. We derive two localization sets for the complementarity eigenvalues of (A, B), the tightest one assuming additionally that A is copositive. This extends He-Liu-Shen sets to the case where B is not the identity. Moreover, we compare the computable bounds obtained from these new sets with the extreme classical generalized eigenvalues.

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Antonio Sasaki, Sophie Demassey, Valentina Sessa. 2026-01-22. Localization of complementarity eigenvalues. https://arxiv.org/abs/2601.15789

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