A very similar technique is popular for rootfinding (since the 80s, convergence analysis in this 1998 paper), where scaling by the norm of the gradient (eq. 1.5

A very similar technique is popular for rootfinding (since the 80s, convergence analysis in this 1998 paper), where scaling by the norm of the gradient (eq. 1.5) enables q-quadratic convergence. https://doi.org/10.1137/S0036142996304796 https://doi.org/10.1137/S0036142996304796 (free version https://repository.lib.ncsu.edu/bitstream/handle/1840.4/296/crsc-tr96-21.pdf https://repository.lib.ncsu.edu/bitstream/handle/1840.4/296/...)