Jacobi-like algorithms for the indefinite generalized Hermitian eigenvalue problem

Mehl, Christian2021-12-172021-12-172002-06-112197-8085https://depositonce.tu-berlin.de/handle/11303/15465http://dx.doi.org/10.14279/depositonce-14238We 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-by-4 subproblems which generalizes the Jacobi-like method of Bunse-Gerstner/Faßbender for Hamiltonian matrices. Furthermore, we discuss structure-preserving Jacobi-like methods based on the solution of non-Hermitian 2-by-2 subproblems. For these methods a local convergence proof is given. Numerical test results for the comparison of the proposed methods are presented.en510 MathematikJacobi-like methodHermitian pencileigenvaluesJacobi-like algorithms for the indefinite generalized Hermitian eigenvalue problemResearch Paper