基于法方程病态的谱修正迭代算法的探讨

Iterative algorithm based on the morbid equation

本文通过分析法方程病态问题产生的原因,结合谱修正迭代算法原理,探讨法方程病态对参数估值的影响,对谱修正迭代的改进算法的适用范围进行扩展,从理论上证明修正因子r取大于零的实数时,迭代改进算法的逆矩阵二范数值随迭代次数的增加而趋近于零,从而得到平差参数接近真值的估值。经过分析发现,谱修正迭代改进算法的迭代速度主要取决于修正因子r和迭代初值的取值。本文从理论和实例证明了迭代速度与修正因子取值保持线性的变化规律,同时用实例证明了不同初值对迭代速度的影响。

In this paper, through analyzing the causes of Ill-posed problems of normal equation which has effect on values of pa- rameters, and combining with iterative algorithm principle of the spectrum correction, it discussed to expand range of the improved al- gorithm. In theory, when correction factor r is greater than zero, two norm of the inverse matrix of the improved algorithm with the in- creasing iteration times is close to zero, so it could get close to the true value parameters of valuations. After analysis, it was proved that the iterative speed depends on the correct factor ＂r＂ and initial iteration value. The result showed that the iterative speed and correction factors keep the change rule of linear values at the same time, and the iteration speed is influenced by the different initial values.