Complex-valued Joint Eigenvalue Decomposition Based on LU Decomposition and Successive Rotations

Abstract

In this paper, we propose a complex-valued joint eigenvalue decomposition(C-JEVD) algorithm based on LU de-composition and successive rotations. The proposed algorithm factorizes the matrix of eigenvectors into a lower-triangular matrix and an upper-triangular matrix, and update these two matrices using successive rotations. In each rotation, the elementary rotation matrix contains only one complex-valued parameter, which could be easily obtained via solving a cubic equation. Therefore, the proposed algorithm has low complexity. The proposed algorithm is compared with other C-JEVD methods through simulations.