Just for the heck of it I decided to try to code Newton’s method today. Basically it’s a way to estimate the roots of a continuous function by using tangents.
Check out the wikipedia article on it if you’ve not heard of it, it’s very cool.
However what I don’t understand about converting it to code is how to determine the derivative for xn+1 = xn - f(xn)/f’(xn)
This (http://z0rch.com/2014/02/09/quick-propagation) article says you can use a secant method to determine the derivative, however that honestly makes no sense to me… From what I understand the secant method is another means to finding the zeroes of a function. Could any math wizards out there provide a little explanation? Thanks.
Edit: Also a quick question, when I worked it out on paper using the aforementioned articles solution I didn’t get the correct answer when I started at 3 with the function x7-1000. Using newton’s method with my own calculated derivative (7x6), I got 2.690 as x3. However the article requires a xn-1; When I’m at x1, what do I use as xn-1 (which would be 0)? Could be a stupid question, sorry if it is.