Application of Eigensolvers in Quadratic Eigenvalue Problems for Brake Systems Analysis

We compare, in terms of computing time and precision, three different implementations of eigensolvers for the unsymmetric quadratic eigenvalue problem. This type of problems arises, for instance, in structural Mechanics to study the stability of brake systems that require the computation of some of the smallest eigenvalues and corresponding eigenvectors. The usual procedure is linearization but it transforms quadratic problems into generalized eigenvalue problems of twice the dimension. Examples show that the application of the QZ method directly to the linearized problem is less expensive that the projection onto a space spanned by the eigenvectors of an approximating symmetric problem, this is not an obvious conclusion. We show that programs where this projection version is quicker may not be so accurate. We also show the feasibility of this direct linearization version in conjunction with an iterative method, as Arnoldi, in the partial solution of very large real life problems.