A class of pseudoinverse-free greedy block nonlinear Kaczmarz methods for nonlinear systems of equations

In this paper, we construct a class of nonlinear greedy average block Kaczmarz methods to solve nonlinear problems without computing the Moore-Penrose pseudoinverse. This kind of methods adopts the average technique of Gaussian Kaczmarz method and combines with the greedy strategy, which greatly reduces the amount of computation. The convergence analysis and numerical experiments of the proposed method are given. The numerical results show the effectiveness of the proposed methods.