New algorithms on Complex Joint Eigenvalue Decomposition Based on Generalized Givens Rotations

In this paper, new joint eigenvalue decomposition (JEVD) methods are developed by considering generalized Givens rotations. These algorithms deal with a set of square complex matrices sharing a same eigen-structure. Several existing methods, using or not generalized Givens rotations, have treated the aforementioned problem. To improve the JEVD solutions, we developed two methods, the first one is numerically stable and efficient but relatively expensive. The second one is developed by considering some justified approximations. Simulation results are provided to highlight the effectiveness and behaviour of the proposed techniques for different scenarios.