Solving generalized inverse eigenvalue problems via L-BFGS-B method

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.