Contour Integration for Eigenvector Nonlinearities
Rob Claes, Karl Meerbergen, Simon Telen · SIAM Journal on Matrix Analysis and Applications · 2023
Abstract. 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.