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Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations. (English) Zbl 1170.65063
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.

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
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