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Homotopy Continuation Methods for Solving Polynomial Multiparameter Eigenvalue Problems
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DOI：10.1007/s11424-026-5445-8.png)
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Abstract
En 中文
Polynomial multiparameter eigenvalue problems (PMEPs) arise in various applications, such as aeroelastic flutter problems, delay differential equations, and ARMA models. The existing methods for solving this problem linearize them as multiparameter eigenvalue problems (MEPs). However, this method is only applicable to specific problems. To the best of our knowledge, there is no method for solving the general PMEPs. This paper presents a homotopy continuation method to find all solutions to PMEPs. The convergence of the method is proved using techniques from algebraic geometry and numerical linear algebra. An acceleration technique for path tracking is also proposed, and numerical results show the effectiveness of the homotopy method.
Keywords:
ARMA model
delay differential equation
homotopy method
polynomial multiparameter eigenvalue problem
polynomial system
Journal
J
IF:
2.8
Papers:
23
Citations:
0
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