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Numerical methods for nonlinear two-parameter eigenvalue problems. (English) Zbl 1342.65116
This paper deals with the nonlinear two-parameter eigenvalue problem (N2EP), which appears in the study of critical delays of delay-differential equations and can be seen as a generalization of both the nonlinear eigenvalue problem (NEP) and the two-parameter eigenvalue problem (2EP). Several numerical methods for NEP, including inverse iteration, residual inverse iteration, successive linear approximation, and Jacobi-Davidson method, are generalized to N2EP. Numerical tests show that the inverse iteration is the most competitive local method and the Jacobi-Davidson method can be used as a global method.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A18 Eigenvalues, singular values, and eigenvectors
Software:
MultiParEig
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