pracma (version 1.7.3)

brent_dekker: Brent-Dekker Root Finding Algorithm

Description

Find root of continuous function of one variable.

Usage

brent_dekker(f, a, b, maxiter = 100, tol = .Machine$double.eps^0.5)

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.

Value

• brent_dekker 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.

Details

brent_dekker 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.

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_dekker(f, 0.6, 1)             # 0.9061798459 correct to 10 places