Nonlinear greedy relaxed randomized Kaczmarz method

Abstract

In this paper, we discuss a nonlinear greedy relaxed randomized Kaczmarz (rNGRK) method for solving large-scale nonlinear problems. This method only needs to calculate one row of the Jacobian matrix in each iteration, which greatly reduces the amount of calculation and storage. Furthermore, the convergence of the rNGRK method is proved and the effectiveness of the rNGRK method in the case of noisy-free data is shown in the corresponding numerical experiments.

Keywords

• Nonlinear equations
• Randomized method
• Greedy method
• Relaxed Kaczmarz method