LU-based Jacobi-like algorithms for non-orthogonal joint diagonalization

In this paper, based on the LU decomposition, we propose three non-orthogonal Jacobi-like alternating iterative algorithms with two strategies for solving the joint diagonalization problem of a set of Hermitian matrices. In this kind of algorithm, each transformation includes one upper triangular iterative step and one lower triangular iterative step, and each step involves one parameter. The optimal parameter of each step is derived analytically. The convergence of our proposed algorithms is proven. According to this convergence analysis, the existing GNJD algorithm is revisited. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed algorithms in comparison with existing ones.