误差估计中矩阵求逆条件数的最优性在Hilbert空间中的推广

The Generation of Optimality in Hilbert Space about Condition Number with Respect to Inversion of Matrix in the Error Estimation

本文利用Ｈｉｌｂｅｒｔ空间中可逆算子的极分解定理，将误差估计中矩阵求逆条件数的最优性在Ｈｉｌｂｅｒｔ空间中进行推广，证明了线性有界算子Ａ的求逆条件数Ｋ（Ａ）＝ＡＡ－１在求算子扰动逆（Ａ＋Ｅ）－１的相对误差界中的极小性质，指出了算子求逆条件数在误差估计中为仅与算子Ａ有关的最佳常数值．

In this paper, the generation of optimality about condition number with respect to inversion of matrix in the error estimation is proved in Hilbert space. it is shown that the condition number K(A) with respect to inversion of Linear bound operator have minimalness in boundary of relative error estimation about inversion ( A+E ) -1 for disturbance of the operator, and is an optimal value, only depands on operator A .