root1d: root1d: Find a single root of a function of one variable...

In rootoned: Roots of one-dimensional functions in R-only code

Description

Find a single root of a function of one variable within a specified interval.

Usage

   root1d(f, interval, tol = .Machine$double.eps^0.5, maxiter = 1000, trace=FALSE, ...) 

Arguments

f	A real function of a single variable.
interval	A vector of two real numbers defining the ends of the interval in which to search.
tol	A tolerance for the root. When the interval within which a root exists is smaller than tol, root1d will terminate.
maxiter	A limit on the number of function evaluations permitted in the attempt to find a root.
trace	If TRUE, provided diagnostic output of the process of rootfinding.
...	Extra data needed to compute the function f.

Details

This routine is an all-R translation of Algorithm 18 of Nash (1979). This is a variant of the Dekker-Brent approach. At the time it was written, the goal was to produce a very short code that was robust in a low-precision environment.

Value

The output is a list consisting of

• root The estimate, b, of the position of the root.

• froot The value of the function at this point, f(b).

• rtol The width of the interval in which the root exists.

• fcount The number of function evaluations used.

References

Nash, John C. (1979) Compact numerical methods: linear algebra and function minimisation. Bristol UK: Adam Hilger.

See Also

optimize

Examples

# Dekker example
# require(rootoned)
dek <- function(x){ 1/(x-3) - 6 }
r1 <- root1d(dek, c(3.0000001, 6), trace=TRUE)
r1

rootoned documentation built on May 2, 2019, 6:48 p.m.