非线性不适定算子方程算子与右端项皆有扰动的Landweber迭代法

LANDWEBER ITERATION FOR NONLINEAR ILL-POSED PROBLEM WITH PERTURBED OPERATOR AND NONEXACT RIGHT-HAND

考虑非线性算子方程 F（x）=y（1）其中 F:D（F） X→Y,X,Y为 Hilbert空间.F是 Frechet可微的。 这里考虑算子方程的解x+不连续依赖于右端数据的情况。由于不稳定性,并且在实际问题中只有近似数据yδ满足 ‖yδ-y‖≤δ（2）可以得到,方程（1）必须正则化.

The Landweber iterative method is studied for solving nonlinear ill-posed problems with both operator and right-hand nonexact. Under certain conditions, the convergence of the method is proved according to a generalized discrepancy principle. Finally, numerical tests are carried out for inverse problem of one-dimensional wave equation.