bisectj: Rootfinding Through Bisection
In rootoned: Roots of one-dimensional functions in R-only code

Description Usage Arguments Details Value References See Also Examples

Finding roots of univariate functions in bounded intervals.

bisect(f, a, b, maxiter = 100, tol = NA, ...)

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

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

`f`	Function or its name as a string.
`a, b`	interval end points.
`maxiter`	maximum number of iterations; default 100.
`tol`	absolute tolerance; default `eps^(1/2)`
`...`	Additional arguments to f()

“Bisection” is a well known root finding algorithms for real, univariate, continuous functions. Bisection works in any case if the function has opposite signs at the endpoints of the interval.

bisect stops when floating point precision is reached, attaching a tolerance is no longer needed. This version is trimmed for exactness, not speed. Special care is taken when 0.0 is a root of the function. Argument 'tol' is deprecated and not used anymore.

“Regula falsi” combines bisection and secant methods. The so-called ‘Illinois’ improvement is used.

Return a list with components root, f.root, the function value at the found root, iter, the number of iterations done, and root, and the estimated accuracy estim.prec

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

ridders

bisect(sin, 3.0, 4.0)
# $root             $f.root             $iter   $estim.prec
# 3.1415926536      1.2246467991e-16    52      4.4408920985e-16

bisect(sin, -1.0, 1.0)
# $root             $f.root             $iter   $estim.prec
# 0                 0                   2       0

# Legendre polynomial of degree 5
lp5 <- c(63, 0, -70, 0, 15, 0)/8

f <- function(x) {pracma::polyval(lp5, x)}
bisect(f, 0.6, 1)       # 0.9061798453      correct to 15 decimals
regulaFalsi(f, 0.6, 1)  # 0.9061798459      correct to 10 decimals