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.

翻译：针对非线性方程组的求解问题，本文发展了一类平均块非线性Kaczmarz方法。在适当假设下建立了该方法的收敛理论，并导出了采用恒定步长和自适应步长时收敛率的上界。数值实验验证了所提方法的高效性，其在迭代步数和计算成本方面均优于现有非线性Kaczmarz方法。