Cubic Eigenvalue Problems

In this paper, we observe cubic eigenvalue problems, which belong to a special class of nonlinear eigenvalue problems. Degree of a cubic eigenvalue problem is relatively small, which allows us to determine some important properties of these problems. We present an algorithm to determine whether a cubic pencil is hyperbolic or not. Also, a definite cubic pencils will be considered. We use a variational characterization as a tool for solving cubic eigenvalue problems and compare the results with the application of the linearization method.