newtonraphson function

A function of the Newton-Raphson algorithm.

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

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.

Returns

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)