Jarlebring, Elias; Hochstenbach, Michiel E. Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations. (English) Zbl 1170.65063 Linear Algebra Appl. 431, No. 3-4, 369-380 (2009). The authors introduce a new type of eigenvalue problem, the polynomial two-parameter eigenvalue problem, with the quadratic two-parameter eigenvalue problem as a special case to analyze the asymptotic stability of delay-differential equations. This framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods. They also recognize a few new matrix pencil variants to determine the asymptotic stability of delay-differential equations. Reviewer: Srinivasan Natesan (Assam) Cited in 19 Documents MSC: 65L07 Numerical investigation of stability of solutions to ordinary differential equations 34K20 Stability theory of functional-differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010) 34K25 Asymptotic theory of functional-differential equations 15A22 Matrix pencils 15A18 Eigenvalues, singular values, and eigenvectors Keywords:delay-differential equations; two-parameter eigenvalue problem; multiparameter eigenvalue problem; critical delays; robustness; stability; asymptotic stability; companion form; quadratic eigenvalue problem; polynomial eigenvalue problem; quadratic two-parameter eigenvalue problem; polynomial two-parameter eigenvalue problem; matrix pencil methods × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link References: [1] Atkinson, F. 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