Jarlebring, Elias; Meerbergen, Karl; Michiels, Wim A Krylov method for the delay eigenvalue problem. (English) Zbl 1226.65069 SIAM J. Sci. Comput. 32, No. 6, 3278-3300 (2010). 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. Reviewer: Constantin Popa (Constanţa) Cited in 1 ReviewCited in 28 Documents 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 Keywords:Krylov subspaces; Arnoldi method; delay eigenvalue problems; time-delay systems; nonlinear eigenvalue problems; Chebyshev polynomials; delay-differential equation; Hessenberg matrix Software:Matlab; UMFPACK; DDE-BIFTOOL; JDQR; MUMPS; Chebfun; TRACE-DDE; JDQZ; ARPACK × Cite Format Result Cite Review PDF Full Text: DOI Link