An Arnoldi method for nonlinear eigenvalue problems

Abstract

For the nonlinear eigenvalue problem T(lambda)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure.