Ⅰ类病态系统中的参数优选

Optimization Selection of Parameters in Ⅰ Ill-Conditioned System

通过对Ⅰ类病态产生原因的分析提出了适合参数分组和不分组两种情况下的参数优选方法,即基于投影正交分解的附加参数比较与选择方法和基于QR分解的参数比较与选择方法。前者用伪残差比对附加参数进行排队,该方法的几何意义明确,伪残差比加速了参数的分化,对参数优选有利;后者利用观测矩阵的QR分解得到的上三角矩阵进行观测结构的分析,根据观测结构的优劣决定参数的取舍。最后利用两个算例对新方法进行了验证和说明。

By analyzing the cause of I Ill-condition, two kinds of parameter optimization methods have been provided on grouping parameters or no. One is the method of additional parameters compared and chosen according to projection orthogonal decomposition, the other is the method of parameters compared and chosen according to QR decomposition. The former queues additional parameters in accordance with pseudo-residual ratio and its geometric interpretation is very clear. The pseudo-residual ratio is advantageous to choose parameters because it can accelerate the differentiation of parameters. Analyzing the observation structure of upper triangular matrix R gotten by the result of QR decomposition, the latter decides which parameters are chosen. Finally two illustrative examples are given to test and verification the two methods.