  The nonlinear Kaczmarz method was recently proposed to solve the system of
nonlinear equations. In this paper, we first discuss two greedy selection
rules, i.e., the maximum residual and maximum distance rules, for the nonlinear
Kaczmarz iteration. Then, based on them, two kinds of greedy randomized
sampling methods are presented. Further, we also devise four corresponding
greedy randomized block methods, i.e., the multiple samples-based methods. The
linear convergence in expectation of all the proposed methods is proved.
Numerical results show that, in some applications including brown almost linear
function and generalized linear model, the greedy selection rules give faster
convergence rates than the random ones, and the block methods outperform the
single sample-based ones.
