A class of averaging block nonlinear Kaczmarz methods is developed for the
solution of the nonlinear system of equations. The convergence theory of the
proposed method is established under suitable assumptions and the upper bounds
of the convergence rate for the proposed method with both constant stepsize and
adaptive stepsize are derived. Numerical experiments are presented to verify
the efficiency of the proposed method, which outperforms the existing nonlinear
Kaczmarz methods in terms of the number of iteration steps and computational
costs