R中的Newton-raphson函数(ELI5)

Question

是否需要一些时间来向我解释，一行一行，这个函数如何使用newton raphson方法计算函数的根?以及r代码是如何执行的。尤其是回归部分?

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)]) #
}

目前我已经定义了这样的变量，但我不确定它是否正确:

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

非常感谢任何形式的帮助!

Answer 1

逻辑是找到[function f（x) = 0]的根。但是当这个函数是高阶函数时，我们不能立即解出根，所以我们使用一个程序1000(n)乘以来猜测哪个最接近根。有时这个函数是连续可微的，但有时不是，所以如果我们发现p[]数据收敛于一个精确数，我们得到根，否则不是。

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