LU-based Jacobi-like algorithms for non-orthogonal joint diagonalization. (1st July 2018)

• Record Type: Journal Article
• Authors: Cheng, Guanghui; Li, Shanman; Miao, Jifei; Moreau, Eric
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 1(2018)
• Page Start: 113
• Page End: 124
• Publication Date: 2018-07-01
• Subjects: Matrix joint diagonalization -- Blind source separation -- Hermitian matrix -- LU decomposition; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.04.007
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.