Generalized Givens Rotations Applied to Complex Joint Eigenvalue Decomposition

Abstract

This paper shows the different ways of using generalized Givens rotations in complex joint eigenvalue decomposition (JEVD) problem. It presents the different schemes of generalized Givens rotation, justifies the introduced approximations and focuses on the process of extending an algorithm developed for real JEVD to the complex JEVD. Several Joint Diagonalization problem use generalized Givens rotations to achieve the solution, many algorithms developed in the real case exist in the literature and are not generalized to the complex case. Hence, we show herein a simple and not trivial way to get the complex case from the real one. Simulation results are provided to highlight the effectiveness and behaviour of the proposed techniques for different scenarios.

Keywords

• complex joint eigenvalue decomposition (jevd)
• shear and shrt
• generalized givens rotations
• exact jevd
• approximative jevd