Jacobi-like algorithms for the indefinite generalized Hermitian eigenvalue problem

We discuss structure-preserving Jacobi-like algorithms for the solution of the indefinite generalized Hermitian eigenvalue problem. We discuss a method based on the solution of Hermitian 4 x 4 subproblems which generalizes the Jacobi-like method of Bunse-Gerstner and Fa bender for Hamiltonian matrices. Furthermore, we discuss structure-preserving Jacobi-like methods based on the solution of non-Hermitian 2 x 2 subproblems. For these methods a local convergence proof is given. Numerical test results for the comparison of the proposed methods are presented.