On an unsymmetric eigenvalue problem governing free vibrations of fluid-solid structures

AMS subject classification. 65F15 Abstract. In this paper we consider an unsymmetric eigenvalue problem occurring in fluid-solid vibrations. We present some properties of this eigenvalue problem and a Rayleigh functional which allows for a min-max-characterization. With this Rayleigh functional the one-sided Rayleigh functional iteration converges cubically, and a Jacobi–Davidson type method improves the local and global convergence properties. 1. Introduction. For a wide class of linear selfadjoint operators A: H → H the eigenvalues of the linear eigenvalue problem Ax = λx can be characterized by three fundamental variational principles, namely by Rayleigh’s principle [13], by Poincaré’s minmax characterization [12], and by the maxmin principle of Courant [4], Fischer [5] and Weyl [20]. These variational characterizations of eigenvalues are known to b