病态矩阵参数估计的改进主元加权迭代算法

Improved Pivot Element Weighted Iterative Algorithm of Ill-conditioned Matrix Parameter Estimation

传统测绘数据处理中矩阵求逆的准确性极大地影响最终解算精度。针对测量数据处理常遇到的病态矩阵求逆不稳定,导致精度显著降低等问题,提出一种改进的主元加权迭代法的病态矩阵处理算法。该算法结合传统主元加权迭代法精度高、误差转移法稳定性好的优点,先将误差从解向量转至中间变量,再利用主元加权迭代法求解中间变量,实现更高精度的解算结果。实验表明,改进算法在良态矩阵法方程中解算结果与传统方法一致,在病态矩阵中改进算法精度更高。

In view of the problem that the inverse of the ill matrix was not stable, and the accuracy was significantly lower in measurement data, this paper proposed an algorithm for the processing of ill-conditioned matrix of improved pivot element weighted iterative method. With the advantage of high accuracy of the pivot element weighted iterative method and good stability of the error transfer method, the algorithm transferred the error to the intermediate variable, and achieved the higher accuracy. The experimental data show that the improved algorithm is the same as the traditional method in the solution of the good-conditioned matrix method, and the improved algorithm has higher accuracy than the traditional method in the ill-conditioned matrix.