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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.

MSC:
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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