快速CU三角分解法

Fast CU triangular factorization algorithm

针对传统CU三角分解法进行三角分解时C、U阵因子阵元素需多个数组存放、元素对应关系不清、计算公式繁琐、编程计算效率不高等问题,提出快速CU三角分解法。在新方法中,引入可清晰地体现c、u元素关系的合成阵;应用按列消元模式和极为简单、直观的四角规则分步计算c、u元素,而无需使用繁琐的元素计算公式;根据c、u元素的对应关系,减少相应u元素的计算。新方法简化了CU三角分解法的分解过程、可大大提高编程效率,并提高三角分解的速度。新方法可用于电力系统计算等各工程领域。

For the problems, such as the elements in the factor matrices are stored independently, the ele- ments relations are not clear,the calculating formulas are complicated, and the efficiency for programming is very low in the conventional CU triangular factorization algorithm,a fast CU triangle factorization algo- rithm is presented in the paper. In the new algorithm,a synthetic matrix in which the elements relations are very clear one another has been introduced,the form of Gaussian elimination in column and the four angles rule are used in order to calculate the elements in the matrices C,U in steps and no any calculating formulas used. In addition,according to the elements relations in the matrices C,U,the calculation for the elements in the matrix U can be reduced. In the way, the deeomposing process for the factor matices is simplified and the efficiency for programming and the calculating speed have been increased greatly in the new algorithm. The new algorithm can be used in the field for power systems and for the other engineering ones.