Convergence results of nonlinear problems based on Tikhonov regularization method

Abstract

In this paper, we study the convergent results of Tikhonov regularization method for solving nonlinear ill-posed problems with noisy operator in Banach spaces. And we give the convergent rates while both the right-hand side of the equation and the operator are given approximately errors. Furthermore we prove that the convergent rates depend on the interplay of the solution smoothness and the nonlinearity structure, and obtain concisely variational inequalities results about them.

Keywords:

• Nonlinear ill-posed problem
• variational inequality
• convergent rates
• Tikhonov regularization
• source conditions

2010 MR Subject Classifications:

• 65R20
• 68W25
• 65F22

Disclosure statement

This work does not have any conflicts of interest.

Additional information

Funding

This project is supported by the National Natural Science Foundation of China [grant number 62071262] and K. C. Wong Magna Fund in Ningbo University.