高斯消元法计算技巧的研究及应用

摘要

针对传统高斯消元法中计算公式应用不便以及编程效率不高等问题,提出无需计算公式可直接完成消元计算的四角规则;根据对称矩阵消元过程中元素的变化特点,提出非零元素的快速判断方法.详细地比较分析了"按行消元、逐行规格化"和"逐行规格化、按列消元"的计算过程,指出尽管前者应用更多,但后者其实更为直观、计算效率更高.上述方法对各IEEE节点系统均高效可行,也同样适用于各个工程领域对因子表法、三角分解法等快速求解.%Considering the problems in the traditional Gaussian eliminating method,such as the inconvenience of the applications of calculation formulas and inefficient programming,a four-angle rule is proposed in the paper,which can be directly used to complete the elimination calculations.According to the changing characteristics of the elements in the elimination processes for symmetrical matrices,fast determination method is also been proposed for nonzero ele?ments.In addition,the calculation processes of"elimination by rows and normalization by rows"and"normalization by rows and elimination by columns"are compared and analyzed.It is suggested that even though the former process can be applied widely,the latter is more direct and has higher calculation efficiency in fact.The above methods are all effi?cient and feasible for various IEEE node systems,and they can also be applied to fast solving the algorithms in engineer?ing fields,such as factor analysis algorithm and triangular decomposition algorithm.