Bounds for relative distances of eigenvalues in free vibration analysis

Abstract

In article [Abdel-Aziz, M.R., 2004, Relative perturbation theory for matrix eigenproblems in free vibration analysis (International J. of Computer Mathematics, Vol. 81, No. 4, pp. 505–514) 1], we have introduced bounds for eigenvalues of eigenproblems in free vibration analysis, when the perturbation happens in either the mass matrix or in the stiffness matrix. This article aims to bound the additive and multiplicative relative distances and ,respectively, where λ and μ are eigenvalues and one is the perturbation of the other. These bounds are investigated when the perturbation happens in both the mass and the stiffness matrices.

Numerical experiments show that the investigated bounds are satisfied and their values are depend on the element-wise perturbation of the matrix.

Keywords:

• Eigen formulations
• Relative distances

Additional information

Notes on contributors

Mohammedi R. Abdel-Aziz

On leave from Department of Mathematics, Faculty of Science, Alexandria University, Egypt.