Perturbation analysis of Joint Eigenvalue Decomposition Algorithms

Joint EigenValue Decomposition (JEVD) algorithms are widely used in many application scenarios. These algorithms can be divided into different categories based on the cost function that needs to be minimized. Most of the frequently used algorithms in the literature use indirect least square (LS) criteria as a cost function. In this work, we perform a first order perturbation analysis for the JEVD algorithms based on the indirect LS criterion. We also present closed-form expressions for the eigenvector and eigenvalue matrices. The obtained expressions are asymptotic in the signal-to-noise ratio (SNR). Additionally, we use these results to obtain a statistical analysis, where we only assume that the noise has finite second order moments. The simulation results show that the proposed analytical expressions match well to the empirical results of JEVD algorithms which are based on the LS cost function.