When solving non-linear equations via Newton's method, load increments are often used to improve convergence. In mechanics for example, if the final load in 90N, one could choose 3 load steps of 30N each. At each load step several Newton iteration are used until convergence, and the final converged result is used as the guess for the next load step. What I do not understand is why at the intermediate load steps, convergence is needed and not just for the final load step? Why not take just one or two iterations at each load step (where the change in the solution is significant) and use that as the initial guess for the next one.

Thanks!

Uri