  This paper addresses the challenge of solving large-scale nonlinear equations
with H\"older continuous Jacobians. We introduce a novel Incremental
Gauss--Newton (IGN) method within explicit superlinear convergence rate, which
outperforms existing methods that only achieve linear convergence rate. In
particular, we formulate our problem by the nonlinear least squares with
finite-sum structure, and our method incrementally iterates with the
information of one component in each round. We also provide a mini-batch
extension to our IGN method that obtains an even faster superlinear convergence
rate. Furthermore, we conduct numerical experiments to show the advantages of
the proposed methods.
