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A class of averaging block nonlinear Kaczmarz methods is developed for thesolution of the nonlinear system of equations. The convergence theory of theproposed method is established under suitable assumptions and the upper boundsof the convergence rate for the proposed method with both constant stepsize andadaptive stepsize are derived. Numerical experiments are presented to verifythe efficiency of the proposed method, which outperforms the existing nonlinearKaczmarz methods in terms of the number of iteration steps and computationalcosts.

On averaging block Kaczmarz methods for solving nonlinear systems of equations