# The nonlinear eigenvalue problem *

@article{Gttel2017TheNE, title={The nonlinear eigenvalue problem *}, author={Stefan G{\"u}ttel and Françoise Tisseur}, journal={Acta Numerica}, year={2017}, volume={26}, pages={1 - 94} }

Nonlinear eigenvalue problems arise in a variety of science and engineering applications, and in the past ten years there have been numerous breakthroughs in the development of numerical methods. This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a particular emphasis on their mathematical properties and available numerical solution techniques. Solvers based on Newton’s method, contour…

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Summary
Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by the…