Meerbergen, KarlKarlMeerbergenSchröder, ChristianChristianSchröderVoß, HeinrichHeinrichVoß2020-06-122020-06-122012-07-09Numerical Linear Algebra with Applications 5 (20): 852-868 (2013-10-01)http://hdl.handle.net/11420/6302The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real-valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large-scale problems, we propose new correction equations for a Newton-type or Jacobi-Davidson style method, which also forces real-valued critical delays. We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi-Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large-scale problems arising from PDEs. © 2012 John Wiley & Sons, Ltd.en1099-150620125852868WileyCritical delayDelay-differential equationJacobi-DavidsonNonlinear eigenvalue problemTwo-parameter eigenvalue problemMathematikJournal Article10.1002/nla.1848Other