LU法改善LabVIEW线性方程组求解速度及专用CIN生成

Improving Speed of Solving Linear Equations by LU Method in LabVIEW and Producing Special CIN

介绍了用LU法改善LabVIEW求解线性方程组的方法,对线性方程组分为四种情况,即系数矩阵为上三角、下三角、正定矩阵以及非满秩矩阵。当系数矩阵为上三角时,将增广矩阵中系数矩阵的对角元素进行单位化,可容易求出方程组的解;当系数矩阵为下三角时,可先进行下三角向上三角的转换,然后求解;当系数矩阵为正定矩阵时,则对系数矩阵进行LU分解,然后再求解;第四种情况不进行是否有解的判断或者多个解的求取。最后根据此算法写出C代码,并给出生成CIN的步骤。

The method of improving the speed of solving linear equations by LU method in LabVIEW was introduced. There are four kinds of situations for the system of linear equations, namely, coefficient matrix is upper triangle or lower triangle or positive matrix or no nonsingular matrix. When it is upper triangle, the elements in coefficient matrix＇s diagonal of augmented matrix are united and the linear equations can be solved easily. When it is lower triangle, the lower triangle is transformed into upper triangle and then the linear equations are solved. When it is positive matrix, the coefficient matrix is decomposed by LU method and solved again. For the fourth situation, it will not be judged whether the linear equations have the solution, or the linear equations are not solved. Finally,according to this algorithm, the author wrote the C codes and gave the steps of producing CIN.