pracma (version 1.9.3)

halley: Halley's Root Finding Mathod

Description

Finding roots of univariate functions using the Halley method.

Usage

halley(fun, x0, maxiter = 100, tol = .Machine$double.eps^0.5)

Arguments

fun

function whose root is to be found.

x0

starting value for the iteration.

maxiter

maximum number of iterations.

tol

absolute tolerance; default eps^(1/2)

Value

Return a list with components root, f.root, the function value at the found root, iter, the number of iterations done, and the estimated precision estim.prec

Details

Well known root finding algorithms for real, univariate, continuous functions; the second derivative must be smooth, i.e. continuous. The first and second derivative are computed numerically.

References

http://mathworld.wolfram.com/HalleysMethod.html

See Also

newtonRaphson

Examples

halley(sin, 3.0)        # 3.14159265358979 in the 3 iterations
halley(function(x) x*exp(x) - 1, 1.0)
                        # 0.567143290409784 Gauss' omega constant

# Legendre polynomial of degree 5
lp5 <- c(63, 0, -70, 0, 15, 0)/8
f <- function(x) polyval(lp5, x)
halley(f, 1.0)          # 0.906179845938664