关键词: 联合对角化, 最小二乘标准, QR分解, 盲信源分离, 代数余子式

Abstract:

Two improved efficient algorithms are proposed to reduce the computational load for non-orthogonal joint diagonalization free of singular solutions. In the first improved algorithm, the determinate of the diagonalization matrix is expanded by its current updating column to avoid matrix inverse operation in this computational phase. The other improved algorithm is developed by QR factorization of the column exchanged diagonalization matrix, whose determinate is computed by the product of the diagonal elements of the resulting upper triangular matrix. As a result, the improved algorithms exhibit a low computational load since both of them reduce one matrix inverse operation in comparison to the original one. Finally, numerical simulation results show that the two improved algorithms have a computational load equal to 18.9％ and 13.5％ that of the original algorithm when the objective matrices are of large dimension and number.

Key words: joint diagonalization, least-squares criteria, QR factorization, blind source separation, algebraic cofactor