求解非线性不适定算子方程的一种Landweber迭代法

A Landweber iterative method for solving nonlinear ill-posed operator equation

针对Landweber迭代方法在非线性不适定问题上进行研究.在非线性算子和右端数据皆为近似的前提条件下,基于Frozen Landweber迭代法,提出双扰动的双循环Landweber迭代格式.在一定的条件下,通过证明迭代格式的单调性和收敛性,得出该迭代格式是有效的.

This paper studied on the Landweber iterative method on nonlinear ill-posed problem.On the condition of the nonlinear operator and the right end of the data both being approximate,based on Frozen Landweber iterative method,a double circulation Landweber iterative scheme of double perturbation was put forward.Under certain conditions,through improving the monotonicity and convergence of iterative scheme,it was obtained that the iterative scheme was effective.