newtonraphson {spuRs}

A function of the Newton-Raphson algorithm.

Description

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

Usage

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.

See Also

fixedpoint, bisection

Examples

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)