brentdekker: Brent-Dekker Root Finding Algorithm

In pracma: Practical Numerical Math Functions

Brent-Dekker Root Finding Algorithm

Description

Find root of continuous function of one variable.

Usage

brentDekker(fun, a, b, maxiter = 500, tol = 1e-12, ...)
brent(fun, a, b, maxiter = 500, tol = 1e-12, ...)

Arguments

fun	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.
...	additional arguments to be passed to the function.

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.

See Also

ridders, newtonRaphson

Examples

# 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 12 places

pracma documentation built on Nov. 10, 2023, 1:14 a.m.