# newtonraphson: A function of the Newton-Raphson algorithm. In spuRs: Functions and Datasets for "Introduction to Scientific Programming and Simulation Using R"

## Description

Applies the Newton-Raphson algorithm to find x such that ftn(x)[1] == 0.

## Usage

 `1` ```newtonraphson(ftn, x0, tol = 1e-09, max.iter = 100) ```

## Arguments

 `ftn` the function. `x0` is the initial guess at the fixed point. `tol` distance of successive iterations at which algorithm terminates. `max.iter` maximum number of iterations.

## Value

Returns the value of x at which ftn(x)[1] == 0. If the function fails to converge within max.iter iterations, returns NULL.

## References

Jones, O.D., R. Maillardet, and A.P. Robinson. 2009. An Introduction to Scientific Programming and Simulation, Using R. Chapman And Hall/CRC.

`fixedpoint`, `bisection`

## Examples

 ```1 2 3 4 5 6 7``` ```ftn4 <- function(x) { # returns function value and its derivative at x fx <- log(x) - exp(-x) dfx <- 1/x + exp(-x) return(c(fx, dfx)) } newtonraphson(ftn4, 2, 1e-6) ```

### Example output

```Loading required package: MASS