Third-order derivative-free methods in Banach spaces for nonlinear ill-posed equations

Abstract

We develop three third order derivative-free iterative methods to solve the nonlinear ill-posed oprerator equation F(x) = f approximately. The methods involve two steps and are free of derivatives. Convergence analysis shows that these methods converge cubically. The adaptive scheme introduced in Pereverzyev and Schock (SIAM J Numer Anal 43(5):2060 2076, 2005) has been employed to choose regularization parameter. These methods are applied to the inverse gravimetry problem to validate our developed results. 2019, Korean Society for Computational and Applied Mathematics.