New Algorithms for Solving Nonlinear Eigenvalue Problems
Walter Gander · Computational Mathematics and Mathematical Physics · 2021
To solve a nonlinear eigenvalue problem we develop algorithms which compute zeros of $$\det A(\lambda ) = 0$$ . We show how to apply third order iteration methods for that purpose. The necessary derivatives of the determinant are computed by algorithmic differentiation. Since many nonlinear eigenvalue problems have banded matrices we also present an algorithm which makes use of their structure.