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arXiv · 2208.13420

Structured eigenvalue backward errors for rational matrix polynomials with symmetry structures

Anshul Prajapati·Punit Sharma
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Abstract

We derive computable formulas for the structured backward errors of a complex number $\lambda$ when considered as an approximate eigenvalue of rational matrix polynomials that carry a symmetry structure. We consider symmetric, skew-symmetric, T-even, T-odd, Hermitian, skew-Hermitian, $*$-even, $*$-odd, and $*$-palindromic structures. Numerical experiments show that the backward errors with respect to structure-preserving and arbitrary perturbations are significantly different.

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Anshul Prajapati, Punit Sharma. 2022-08-29. Structured eigenvalue backward errors for rational matrix polynomials with symmetry structures. https://arxiv.org/abs/2208.13420

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