基于值域包含的不适定算子方程的收敛速度

On the Convergence Rate for the Ill-posed Operator Equation Involving Range Inclusion

讨论了不适定的算子方程Af=Bg的收敛速度问题.方程的不适定是指方程的解对初始条件缺乏连续依赖的性质.这里的算子B是定义在某个恰当的Hilbert空间上的算子,它可能是无界算子,而且有值域包含关系R(A)■R(B).

In this paper,we consider the convergence rate of the operator equation Af =Bg,which is ill-posed in the sense that the continuous dependence of the solution to the initial data does not hold,where B is a unbounded operator in some suitable Hilbert space with R（A） （∈）R（B）.