On an extension of A. N. Krylov´s numerical method for determining the frequencies of small vibrations of systems with damping

In many engineering problems we must find the roots of an equation of the form where B(λ) is a nonlinear matrix of λ. In this paper we show how this problem may be reduced to integrating a system of ordinary differential equations subject to known initial conditions. The method covers also the case of complex roots. It gives directly the roots i: without the need of forming and solving the characteristic equation.