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arXiv · 2605.20933

Conditioning and backward errors for nonlinear eigenvalue problems with eigenvector nonlinearities

Vilhelm Peterson Lithell·Victor Janssens·Elias Jarlebring·Karl Meerbergen·Wim Michiels
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Abstract

We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be evaluated with little computational effort for a given eigenpair, assuming the matrix perturbations are measured by the spectral or Frobenius norm. We also show how symmetric perturbations can be exploited in the analysis. By means of two numerical experiments we demonstrate that problems incorporating eigenvector nonlinearities potentially need to be treated with additional care, when compared to the linear or eigenvalue-nonlinear theory.

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Vilhelm Peterson Lithell, Victor Janssens, Elias Jarlebring, Karl Meerbergen, Wim Michiels. 2026-05-20. Conditioning and backward errors for nonlinear eigenvalue problems with eigenvector nonlinearities. https://arxiv.org/abs/2605.20933

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