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We consider a second order damped-vibrational system described by the equation M ¨ x + C(v) ˙ x + Kx = 0, where M, C(v), K are real, symmetric matrices of order n. We assume that the undamped eigenfrequencies (eigenvalues of (λ 2 M + K)x = 0) ω n−1 ≈ ω n. We present a formula which gives the solution of the corresponding phase space Lyapunov equation, which… (More)

We consider a mechanical system excited by an external force. Model of such a system is described by the system of ordinary differential equations: M ¨ x(t) + D(v) ˙ x(t) + Kx(t) = ˆ f (t), where matrices M, K (mass and stiffness) are positive definite and the vectorˆf corresponds to an external force. The damping matrix D(v) is a positive semidefinite… (More)

We consider a mathematical model of a linear vibrational system described by the second-order system of differential equations M ¨ x + D ˙ x + Kx = 0, where M, K and D are positive definite matrices, called mass, stiffness and damping , respectively. We are interested in finding an optimal damping matrix which will damp a certain part of the undamped… (More)

- Ninoslav Truhar, Zoran Tomljanovic, Ren Cang, Zoran Tomljanović
- 2009

The solution to a general Sylvester equation AX −XB = GF * with a low rank right-hand side is analyzed quantitatively through Low-rank Alternating-Directional-Implicit method (LR-ADI) with exact shifts. New bounds and perturbation bounds on X are obtained. A distinguished feature of these bounds is that they reflect the interplay between the eigenvalue… (More)