核素深度分布就地测量中病态线性方程组的迭代解法

在就地γ谱仪地面放射性核素深度分布测量研究中遇到了病态线性方程组的求解问题,方程组系数矩阵条件数达3×10~8.此方程组的求解特殊性在于:一是病态性十分严重,二是保证方程组解的非负性才符合实际.尝试多种解法不奏效的情况下,借助于行列均衡化处理技术、最大似然法非线性方程组建立和相应的EM迭代法,求解获得了满意结果.

Iteration Algorithm of One Linear Ill-conditioned Equation Group for In-situ Measurement of Radionuclide-depth-distribution

In our work of in-situ measurement of radionuclide-depth-distribution with in-situ HPGe γ spec-trometry, a linear ill-conditioned equation group exists, whose coefficient matrix has big conditional value 3×10~8. It is difficult to obtain the true solution for that it is high ill-conditioned and the nonnegative solu-tion is required. Many usual solution methods are invalidated. So an effectual EM iteration algorithm method is approached in the paper, which includes three steps: coefficient-matrix-equalization processing,maximum-likelihood processing, and EM-iteration-algorithm establishment. By the solution method pres-ented the true solution was obtained with the approving precision.