降低计算量的改进联合对角化算法

提出两种改进算法解决避免奇异解的联合对角化算法计算量大的问题。一方面,将对角化矩阵行列式按当前更新的列直接展开得到一种改进算法;另一方面,将列交换后的对角化矩阵进行LU分解,由分解得到的上(下)三角矩阵计算行列式,得到了另一种改进算法。由于两种改进算法都减少了一次矩阵求逆,因此降低了原算法的计算量。实验仿真表明,当目标矩阵的个数和维数较大时,两种改进算法的计算量分别为原算法的36.8%和21.5%。

Improved joint diagonalization algorithm with low computational load

Two improved algorithms for non-orthogonal joint diagonalization free of degenerate solutions are presented to reduce the computational load of the original algorithm.On one hand,the determinant of the diagonalization matrix is directly expanded via its current updating column to reduce one matrix inverse operation.On the other hand,the other improved algorithm is developed by LU factorization of the column exchanged diagonalization matrix.As a result,the improved algorithms are computationally inexpensive since both of them reduce one matrix inverse operation in comparison with the original one.In the end,the computer simulation results show that two improved algorithms have a reduced computational load which is equal to 36.8% and 21.5% of that of the original one respectively when the number and dimension of the objective matrix are relatively large.