摘要
在用牛顿迭代法求解非线性算子方程时,总要求非线性算子的导算子是有界可逆的,即线性化方程是适定的.但在实际数值计算中.即使满足这个条件,也可能出现数值不稳定的现象.为了克服这个困难,[1]将牛顿法与求解线性不适定问题的BG方法(平均核方法)结合起来,在每一步迭代中利用BG方法稳定求解.
In this paper, Newton's methods for solving nonlinear operator equations and Tikhonov'sregularization method for solving linear ill-posed problems are combined into two new iterativemethods for solving nonlinear operator equations with ill-conditioned Frechet derivatives. Someresults about their convergence and error estimates are obtained. The applicabilities of these me-thods to solving inverse problems of difference equations are demonstrated. It is shown by nu-merical simulations that these methods are feasible and effective.
出处
《计算数学》
CSCD
北大核心
1990年第3期225-231,共7页
Mathematica Numerica Sinica
