求解非线性不适定问题的连续Landweber型正则化方法(英文)

Continuous Landweber type regularization method for solving nonlinear ill-posed problem

提出一种用于求解非线性不适定问题的连续Landweber型正则化方法。在假定解是光滑的前提下,证明该方法的收敛性和稳定性。数值模拟表明,对该方法离散化后可得到二阶迭代格式,方法稳定,且在较少的迭代步数内收敛。

A continuous Landweber type regularization method for solving nonlinear ill-posed prob- lems is proposed. Under the smoothness of the unknown solution, convergence and stability of the asymp- totical regularization method are given. Moreover, some numerical experiments are presented to illustrate that the 2-stage iterative regularization methods are stable and efficient in saving iteration steps.