R secant method

secant.R

library(ggplot2)

secant <- function(fn) {
    a <- -100
    b <- 100
    for (i in 1:1000) {
        numerator <- b * fn(a) - a * fn(b)
        denominator <- fn(a) - fn(b) + 1e-9
        x <- numerator / denominator
        a <- b
        b <- x
    }
    x
}

x <- -100:100
fn <- function(x) {
    x + x ^ 2
}
temp <- data.frame(x = x, y = fn(x))
ggplot(data = temp, aes(x = x, y = y)) + geom_line() + geom_vline(xintercept = secant(fn),
                                                                  colour = "red",
                                                                  linetype = "dashed")