On pseudoinverse-free block maximum residual nonlinear Kaczmarz method for solving large-scale nonlinear system of equations

Recently, motivated by works arising from large-scale linear systems, some stochastic and deterministic nonlinear Kaczmarz (NK) methods have been developed to solve large-scale nonlinear system of equations. In this paper, based on row sample with an approximate maximum residual control criterion, we propose a pseudoinverse-free block maximum residual nonlinear Kaczmarz (FBMRNK) method for solving large-scale nonlinear system of equations. Then we show that FBMRNK is a variant of the sketched Newton-Raphson (SNR) method with an adaptive sketching matrix. Furthermore, using this connection we establish the global convergence theory of FBMRNK with mu-strongly quasi-convexity or star-convexity. Finally, numerical results are provided to demonstrate superior performance of FBMRNK to the stochastic or deterministic nonlinear Kaczmarz-type methods.