We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial eigenvalue problems, which are solved as generalized eigenvalue problems. Our general approach avoids the need for custom linearizations of PMEPs. We provide rigorous theoretical guarantees for generic PMEPs and give practical strategies for nongeneric systems. Benchmarking on applications from aeroelastic flutter and leaky wave propagation confirms that our algorithm attains high accuracy and robustness while being broadly applicable to many PMEPs.

翻译：本文提出了一种新颖的全局算法，用于求解多项式多参数特征值问题（PMEPs），其核心在于利用隐变量张量Dixon结式框架。该方法将PMEP转化为一个或多个单变量多项式特征值问题，并作为广义特征值问题进行求解。我们的通用方法避免了为PMEPs定制线性化方案的需要。我们为一般性PMEPs提供了严格的理论保证，并针对非一般性系统给出了实用的求解策略。在气动弹性颤振和漏波传播等应用上的基准测试证实，该算法在广泛适用于多种PMEPs的同时，实现了高精度与强鲁棒性。