线性方程组迭代解的随机模型测试研究

EVALUATION ON THE ITERATIVE SOLUTION OF LARGE LINEAR EQUATION WITH MODELING CHECKER METHOD

本文讨论大型线性方程组迭代解的随机模型测试评价问题。给出了常用迭代解法ＣＧ、ＬＳＱＲ、ＳＩＲＴ、ＳＡＲＴ、ＳＡＳＩＲＴ等的测试结果。结果表明：（１）方程组系数矩阵的特性（条件数）及解结构都对解精度有重要影响。解模型越粗糙，解的精度越低。（２）各种求解算法都有一定的平滑效应，同时各种算法也都会产生误差大于２００％的奇异解，奇异解元素数一般约占１０％。（３）数据的拟合残差一般不能真实反映解的精度。（４）对含误差数据的求解问题，较好的求解算法是ＤＬＳＱＲ与ＳＡＳＩＲＴ。

A modeling checker method for the evaluation of the iterative solution of large liner system of equations is introduced in this paper. Some algorithms in common use are verified using the method and the test data show that:(1) both the singularity of the coefficient matrix and the style of the solution model(physical model)have effects on the reliability and the precision of the solution; the rougher the solution model, the less the reliability and the precision of the solution is; (2) each iterative algorithm has smoothing effect and may, at same time, export some singularity solution elements with an error more than 200%, about 10% out of the total) ; (3) The error of the data misfit is not always consistent with the error of the solution; (4) when the data contain some errors, DLSQR and SASIRT are the better algorithms to solve the linear equation system.