Abstract:
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.
Key words:nonlinear eigenvalue problem, third order methods, algorithmic differentiation.
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