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Nonlinear Systems, Cont'd
Given initial guess, must evaluate matrix elements and RHS, solve system for , and compute next iteration xi+1. Then repeat (must solve 2 2 linear system each time).
Essentially the non-linear system has been linearized to make it easier to work with.
NriC 9.7 discusses a global convergence strategy that combines multi-D NR with "backtracking" to improve chances of finding solutions.