ABSTRACT The parameterized generalized inverse eigenvalue problems containing multiplicative and additive inverse eigenvalue problems appear in vibrating systems design, structural design, and inverse Sturm–Liouville problems. In this article, by using the Cholesky factorization and the Jacobi method, we propose two efficient algorithms based on Newton's method and the L-BFGS-B method for solving these problems. To demonstrate the effectiveness of the algorithms, we present three numerical examples.

中文翻译：

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通过 L-BFGS-B 方法求解广义逆特征值问题

摘要 包含乘法和加法逆特征值问题的参数化广义逆特征值问题出现在振动系统设计、结构设计和逆 Sturm-Liouville 问题中。在本文中，通过使用 Cholesky 分解和 Jacobi 方法，我们提出了两种基于牛顿法和 L-BFGS-B 方法的有效算法来解决这些问题。为了证明算法的有效性，我们给出了三个数值例子。