Solving nonlinear inverse problems by evolution equations based on Gauss–Newton methods

Abstract

In this article, we solve nonlinear inverse problems by an evolution equation method which can be viewed as the continuous analogue of the Gauss–Newton method. Under certain conditions we prove the convergence and derive the rate of convergence when the discrepancy principle is coupled.

Keywords:

• nonlinear inverse problems
• evolution equation based on Gauss–Newton method
• the discrepancy principle
• convergence
• rates of convergence

AMS Subject Classifications::

• 65J15
• 65J20
• 47H17