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

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.

Keywords:

• Inverse eigenvalue problem
• parameterized generalized inverse eigenvalue problems
• Cholesky factorization
• L-BFGS-B method
• Jacobi rotation
• Newton's method

AMS MSC 2010:

• 65F18
• 49M15

Acknowledgements

The authors are deeply grateful to the editor and anonymous referees for helpful comments and suggestions which led to a significant improvement of the original manuscript of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.