病态线性方程组的简单迭代解法

针对地球物理反问题中经常碰到的病态线性方程组的求解问题。本文提出了一种简单迭代（ＳＩ）算法，从理论上证明了解序列收敛且收敛到方程组的真解，然后给出了几个算例，将计算结果与对付病态问题能力很强的ＣＧ类算法的结果进行了对比，结果表明：ＳＩ算法具有极强的抗病态能力，计算精度明显高于ＣＧ类算法，但计算速度稍低于后者

A SIMPLE ITERATION ALGORITHM FOR MORBID STATE LINEAR EQUATION GROUP

A simple iteration (SI) algorithm for morbid state linear equation group often existed in geophysical inversion problem is put forward in this paper. First, the authors prove theoretically that the solution series obtained with iterating method are convergent and are converged to the true solution of the original equation set. Then the authors give some numerical examples to compare with the results obtained with the conjugate gradient(CG) algorithm. The results of comparison show that SI is very powerful in treating the problem of morbid state linear equation group, and its calculation accuracy is obviously higher than that of CG algorithm, and that its compution velocity is only slightly slower than that of CG algorithm.