R: One Dimensional Root (Zero) Finding

uniroot {base} | R Documentation

## One Dimensional Root (Zero) Finding

### Description

The function `uniroot` searches the interval from `lower` to `upper` for a root (i.e. zero) of the function `f` with respect to its first argument.

### Usage

    uniroot(f, interval, lower = min(interval), upper = max(interval),
            tol = .Machine$double.eps^0.25, maxiter = 1000, ...)

### Arguments

`f` | the function for which the root is sought.
`interval` | a vector containing the end-points of the interval to be searched for the root.
`lower` | the lower end point of the interval to be searched.
`upper` | the upper end point of the interval to be searched.
`tol` | the desired accuracy (convergence tolerance).
`maxiter` | the maximum number of iterations.
`...` | additional arguments to `f`.

### Details

Either `interval` or both `lower` and `upper` must be specified. The function uses Fortran subroutine ``"zeroin"`' (from Netlib) based on algorithms given in the reference below.

If the algorithm does not converge in `maxiter` steps, a warning is printed and the current approximation is returned.

### Value

A list with four components: `root` and `f.root` give the location of the root and the value of the function evaluated at that point. `iter` and `estim.prec` give the number of iterations used and an approximate estimated precision for `root`.

### References

Brent, R. (1973) Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice-Hall.

### See Also

`polyroot` for all complex roots of a polynomial; `optimize`, `nlm`.

### Examples

    f <- function (x,a) x - a
    str(xmin <- uniroot(f, c(0, 1), tol = 0.0001, a = 1/3))
    str(uniroot(function(x) x*(x^2-1) + .5, low = -2, up = 2, tol = 0.0001),
        dig = 10)
    str(uniroot(function(x) x*(x^2-1) + .5, low = -2, up =2 , tol = 1e-10 ),
        dig = 10)

    ## Find the smallest value x for which exp(x) > 0 (numerically):
    r <- uniroot(function(x) 1e80*exp(x) -1e-300,,-1000,0, tol=1e-20)
    str(r, digits= 15)##> around -745.1332191

    exp(r$r)        # = 0, but not for r$r * 0.999...
    minexp <- r$r * (1 - .Machine$double.eps)
    exp(minexp)     # typically denormalized

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