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A Krylov method for the delay eigenvalue problem. (English) Zbl 1226.65069
The authors propose a generalization of the Arnoldi method to the characteristic equation of a delay-differential equation, namely the delay eigenvalue problem. They derive a new method by applying the Arnoldi method to the generalized eigenvalue problem associated with a spectral discretization of the operator; their method yields the same Hessenberg matrix as the Arnoldi method applied to the operator.

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34L30 Nonlinear ordinary differential operators
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