Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization of these methods which leads to a contour integration approach for computing all eigenvalues of a PEPv in a compact region of the complex plane. Our methods can be used to solve any suitably generic system of polynomial or rational function equations.

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SIAM Journal on Matrix Analysis and Applications
New frontiers in numerical nonlinear algebra
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Claes, R., Meerbergen, K., & Telen, S. J. L. (2023). Contour integration for eigenvector nonlinearities. SIAM Journal on Matrix Analysis and Applications, 44(4), 1619–1644. doi:10.1137/22M1497985