数值求解迭代Tikhonov正则化方法的一点注记

A NOTE ON NUMERICAL SOLUTION OF ITERATED TIKHONOV REGULARIZATION

（?）1.引 言 我们考虑如下形式的不适定算子方程 Af=g,（1）其中 A:F→G为一个有界线性算子,F,G为Hilbert空间.通常右端项g为“观测数据”,因而不可避免地带有一定的误差δ,即我们所得到的数据为gδ,满足:||g—gδ||≤δ.有时即使A-1:Range（A）→F存在,但也未必连续,因而数值求解相当不稳定[2,3].消除不稳定性的一个自然的方式是用一簇接近适定问题的模型去逼近原问题,比如说最著名的Tikhonov正则化方法,用如下适定的算于方程 （A＊A+αI）fα=A＊gδ（2）

In practical applications we often encounter ill-posed operator equations. So far, explicit methods or direct methods and implicit methods or indirect methods have been well developed for solving such problems. This paper deals with the numerical implementation of such problems and proposes a efficient algorithm for implementing implicit methods.