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i was wondering how this user managed to use newton's method to approximate an actual function (that being the lambert w function) rather than its roots.

i cannot seem to follow his logic, and through my research i have only come across examples of people using newtons method to approximate the roots of a function, not the function itself.

how could i use what he has done to approximate, say, ln(x) in a similar manner?

PythonNoob
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  • This works if the Newton sequence converges pointwise to the solution. In this case , we can actually iterate the complete function and get after some iterations a more or less good approximation. – Peter Nov 28 '22 at 07:31
  • @Peter forgive me, but could you explain this in layman's terms? or give another example of a function with this property? i apologize for my inexperience with the subject – PythonNoob Nov 28 '22 at 13:15

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