Fast Approximate Joint Diagonalization of Positive Definite Hermitian Matrices

Abstract

In this paper, a new efficient iterative algorithm for approximate joint diagonalization of positive-definite Hermitian matrices is presented. The proposed algorithm, named as SVDJD, estimates the diagonalization matrix by iterative optimization of a maximum likelihood based objective function. The columns of the diagonalization matrix is not assumed to be orthogonal, and they are estimated separately by using iterative singular value decompositions of a weighted sum of the matrices to be diagonalized. The performance of the proposed SVDJD algorithm is evaluated and compared to other existing state-of-the-art algorithms for approximate joint diagonalization. The results imply that the SVDJD algorithm is computationally efficient with performance similar to state-of-the-art algorithms for approximate joint diagonalization.