brentdekker: Brent-Dekker Root Finding Algorithm

Description

Find root of continuous function of one variable.

Usage

 ```1 2``` ```brentDekker(f, a, b, maxiter = 100, tol = .Machine\$double.eps^0.75) brent(f, a, b, maxiter = 100, tol = .Machine\$double.eps^0.75) ```

Arguments

 `f` function whose root is to be found. `a, b` left and right end points of an interval; function values need to be of different sign at the endpoints. `maxiter` maximum number of iterations. `tol` relative tolerance.

Details

`brentDekker` implements a version of the Brent-Dekker algorithm, a well known root finding algorithms for real, univariate, continuous functions. The Brent-Dekker approach is a clever combination of secant and bisection with quadratic interpolation.

`brent` is simply an alias for `brentDekker`.

Value

`brent` returns a list with

 `root` location of the root. `f.root` funtion value at the root. `f.calls` number of function calls. `estim.prec` estimated relative precision.

References

Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.

`ridders`, `newtonRaphson`

Examples

 ```1 2 3 4``` ```# Legendre polynomial of degree 5 lp5 <- c(63, 0, -70, 0, 15, 0)/8 f <- function(x) polyval(lp5, x) brent(f, 0.6, 1) # 0.9061798459 correct to 10 places ```

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