A Perturbation Method for Index Detection for Linear Matrix Pencils
Numerical Analysis
2026-03-24 v1 Numerical Analysis
Abstract
Rigorous, non-asymptotic bounds for the Puiseux expansion of the eigenvalue at infinity are given. Error analysis is provided. Further, the expected value of the eigenvector condition number of a randomly perturbed matrix is estimated. The latter result is applied to the Cayley transform of the linear pencil. Numerical simulations illustrating the theoretical findings are provided.
Keywords
Cite
@article{arxiv.2603.21771,
title = {A Perturbation Method for Index Detection for Linear Matrix Pencils},
author = {Hanna Blazhko and Michał Wojtylak},
journal= {arXiv preprint arXiv:2603.21771},
year = {2026}
}