Bounds for relative distances of eigenvalues in free vibration analysis
Mohammedi R. Abdel‐Aziz · International Journal of Computer Mathematics · 2005
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 Abdel-Aziz, M. R. 2004. International Journal of Computer Mathematics, 81(4): 505–514. [Taylor & Francis Online] , [Google Scholar]], 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.