A residual-based weighted nonlinear Kaczmarz method for solving nonlinear systems of equations

A novel nonlinear Kaczmarz method is proposed for solving large-scale nonlinear problems, which adaptively uses residual to combine the Jacobian submatrix and projects onto the weighted hyperplane. The convergence theory of the new method is proved, and the upper bound of the convergence rate is well studied. Numerical experiments are given to demonstrate that the proposed method is efficient and better than the existing methods in terms of the number of iterations and CPU time.