The real polynomial eigenvalue problem is well conditioned on the average
arXiv:1802.0749313 citationsh-index: 20
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Provides theoretical guarantees for the numerical stability of polynomial eigenvalue problems, relevant to numerical linear algebra and scientific computing.
The paper studies the average condition number for polynomial eigenvalues of random matrix ensembles, proving that polynomial eigenvalue problems with Gaussian entries are very well-conditioned on average.
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.