Cone Rayleigh Levels: Finite Perturbations and Certified Control
We study the reuse of positive trial profiles under finite perturbations of nonsymmetric matrix pencils B-λG. The lower and upper cone Rayleigh levels need not coincide and are defined without requiring positive eigenvectors. In the positive orthant with positive diagonal $G$, we derive computable perturbation bounds and determine the exact worst-case trial gap over prescribed independent entrywise perturbation classes. This yields the largest uniform radius meeting a given trial-gap tolerance for fixed profiles, certifying trial-value accuracy without recomputation. Experiments on a nonnegative operator and five signed matrices compare sufficient and optimal radii, directional thresholds...
| Authors | Yavdat Sh. Il'yasov, Nur F. Valeev |
|---|---|
| Primary category | cs.LG |
| Published | 27 August 2026 |
| Last updated at source | 5 October 2026 |
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