On structured condition number of rational matrix functions
Optimization and Control
2025-09-26 v1
Abstract
We derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations. We obtain an exact expression for the structured condition number of simple eigenvalues of symmetric, skew-symmetric and even/odd rational matrix functions, and tight bounds are obtained for simple eigenvalues of Hermitian, skew-Hermitian, even/odd, and palindromic rational matrix functions.
Cite
@article{arxiv.2509.21101,
title = {On structured condition number of rational matrix functions},
author = {Ritwik Prabin Kalita and Anshul Prajapati and Punit Sharma},
journal= {arXiv preprint arXiv:2509.21101},
year = {2025}
}
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22 pages