# 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.

## 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
Loading required package: lattice
At iteration 1 value of x is: 1.12202
At iteration 2 value of x is: 1.294997
At iteration 3 value of x is: 1.309709
At iteration 4 value of x is: 1.3098
Algorithm converged
[1] 1.3098

spuRs documentation built on May 21, 2018, 9:03 a.m.