牛顿-拉夫森 function 在 R (ELI5)

Question

Would something take a few moments to explain to me, line by line, how this function calculates the root of a function using the newton raphson method? And how the r code is executing that. Especially the return-part?

newton <- function(f, delta = 0.0000001, x_0 = 2, n=1000){
  h = 0.0000001
  i = 1; x1 = x_0
  p = numeric(n)
  while (i <= n) { 
    df.dx = (f(x_0 + h) - f(x_0)) / h
    x1 = (x_0 - (f(x_0) / df.dx)) 
    p[i] = x1 
    i = i+1 
    if (abs(x1 - x_0) < delta) break 
    x_0 = x1
  }
  return(p[1: (i-1)]) #
}

Currently I've defined the variables like this but I'm not sure if it is correct:

f = the function we input
delta = the accuracy threashold we are willing to accept
x_0 = our initial guess
n = the number of iterations
h = the distance from original guess to true root
abs = the current value of the function

Thanks a million for any sort of help!

Answer 1

The Logic is find [ function f（x) = 0 ]'s roots。but we can't solve the root immediately when this function is Higher Order,so we use a program 1000(n) times to guess which one is closest to the root. Sometimes this function is continuously differentiable，but sometimes not, so if we found p[] data is convergent to a accuracy number, we get the root, else not.

f = the function we input (Y)
delta = the accuracy threashold we are willing to accept (Y)
x_0 = our initial guess (Y)
n = the number of iterations (Y)
h = the distance from original guess to true root (N) 
h = the distance from X1 to X0,this value much little ,the root much closed.
abs = the current value of the function (N)
abs is a sys