避免奇异解联合对角化的两种高效算法

Abstract

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

CLC Number:

TN911.7

ZHANG Wei-tao;LIU Ning;LOU Shun-tian. Two efficient algorithms for joint diagonalization with exception of the singular solution[J].J4, 2009, 36(5): 857-861.

References

joint diagonalization|least-squares criteria|QR factorization|blind source separation|algebraic cofactor
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Two efficient algorithms for joint diagonalization with exception of the singular solution

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