When Newton's method doesn't work

so...if Newton's method doesn't work...which is the alternative?

That was really helpful. Thank you

how could i choose the intial point for non linear system is there asort of wayor method for doing that

Make sure:
1. That the function is differentiable.
2. That you don't devide by 0 with f'(x)
3. That your first guess is good.

The bottom line is... if you're not an idiot Newton's method will work.