@LuaiGhunim There are lots of ways Newton's method can fail. It could be that your function is non-smooth and doesn't have a well-defined Jacobian. It could be that the Jacobian is just difficult to approximate because sometimes you don't have the analytic expressions for the partial derivatives and you use finite differences. It could be that the convergence is just really slow. The Jacobian could be near-singular which makes it a pain to invert the Jacobian. The condition number can be enormous and errors can overwhelm your accuracy and precision.
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