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A. C. Antoulas and D. C.Sorensen, “Lyapunov, Lanczos and Inertia,” Linear Algebra and Its Applications, Vol. 326, No. 1-3, 2001, pp. 137-150. doi:10.1016/S0024-3795(00)00288-3

has been cited by the following article:

• TITLE: Analyzing the Stability of a n-DOF System with Viscous Damping

  AUTHORS: Hashem Saberi Najafi, Amir Hosein Refahi Sheikhani

  KEYWORDS: n-DOF System, Inertia, Stability, Lanczos

  JOURNAL NAME: Applied Mathematics, Vol.2 No.8, August 3, 2011

  ABSTRACT: In this paper we introduce a numerically stable method for determining the stability of n-DOF system without computing eigenvalues. In this sense, at first we reduce the second-order system to a standard eigenvalue problem with symmetric tridiagonal form. Then we compute the exact inertia by using an algorithm based on floating point arithmetic [1]. Numerical tests report the effectiveness of these methods.