Purpose
To work out Exercise 13.4
> library(polynom)
> coefs <- c(-1, -2, 3, -3, -2, 1)
> p <- polynomial(coef = coefs)
> p1 <- deriv(p)
> p.f <- as.function(p)
> p1.f <- as.function(p1)
> x <- 0
> y <- p.f(x)
> xs <- vector()
> for (i in 1:6) {
+ x <- x - y/p1.f(x)
+ y <- p.f(x)
+ print(paste(x, y, sep = " "))
+ xs <- c(xs, x)
+ }
[1] "-0.5 0.96875"
[1] "-0.336842105263158 0.0986450190238757"
[1] "-0.315728448396289 0.00191853843116618"
[1] "-0.315301162703277 7.90693466257153e-07"
[1] "-0.315300986459363 1.34559030584569e-13"
[1] "-0.315300986459333 0" |
> par(mfrow = c(1, 1))
> plot(p)
> abline(h = 0)
> abline(v = 0) |
![Lect_13_3-002.jpg](images/lect_13_3-002.jpg)
The first 6 digits are
> print(xs, digits = 16)
[1] -0.5000000000000000 -0.3368421052631579 -0.3157284483962894
[4] -0.3153011627032768 -0.3153009864593627 -0.3153009864593327
> solve(p)[2]
[1] -0.3153009864593327+0i |