各种三角分解法计算特性的分析比较

Analysis and comparison on the calculating characteristics of triangular decomposition algorithms

通过对LR、LDU、CU3种三角分解法的计算原理和计算过程,包括中间变量的计算、所需计算元素的个数、所需元素的总数等进行详细地比较分析,并将3种三角分解法分别编程用于求解IEEE-30、-57、-118节点系统的节点阻抗矩阵,比较其"分解"及"分解+回代"过程所需的计算时间。原理分析和计算结果均表明,LR、CU与LDU三角分解法相比,计算过程更为简洁,计算速度远快于LDU三角分解法,且CU三角分解法的计算速度略快于LR三角分解法,计算原理和方式非常接近高斯消元法。因此,在用三角分解法求解常系数的线性方程组时,应该首选CU三角分解法而不是其它三角分解法。

The detailed calculating principle and the processes for the triangular decomposition algorithms,i. e. ,LR,LDU, CU algorithms, including the middle variable, the numbers of elements calculated, the total numbers of elements for calculating, have been analyzed in the paper. The algorithms were used to program and calculate the impedance matrix of IEEE-30,- 57,- 118 bus systems. We compared the calculating times of the ＂decomposing＂ and the ＂decomposing＋back substitution＂. The calculating principle and the results indicated that the LR and CU algorithms were simpler and faster than the LDU algorithm. Besides, the calculating speed of the CU algorithm was faster than the LR algorithm＇. Therefore, when solving the constant coefficient equations with a triangular decomposition algorithm,the CU algorithm should be firstly used instead of other triangular decomposition algorithms.