The real polynomial eigenvalue problem is well conditioned on the average

TL;DR

This paper investigates the average conditioning of polynomial eigenvalue problems, demonstrating that problems with Gaussian matrices are typically well-conditioned, which has implications for numerical stability in computations.

Contribution

It provides a rigorous analysis showing that polynomial eigenvalue problems with Gaussian matrices are well-conditioned on average, a novel insight into their numerical stability.

Findings

Polynomial eigenvalue problems with Gaussian matrices are well-conditioned on average.

The study extends understanding of numerical stability in polynomial eigenvalue computations.

Results suggest robustness of solutions for random matrix ensembles.

Abstract

We study the average condition number for polynomial eigenvalues of collections of matrices drawn from various random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with Gaussian entries are very well-conditioned on the average.