On the Numerical Solution of (λ² A + λ B + C), x = b and Application to Structural Dynamics

In this paper we address the numerical solution of a large linear system depending quadratically on a parameter that varies in a wide range. We analyze a solution method, whose computational cost grows only sublinearly with the number of parameters, that relies on the use of an indefinite inner product. Important implementation aspects are treated in detail. The problem arises in various application areas: we shall report on our experience with cases in structural dynamics.