Find the root of the function f — itp

This finds the value \(x \in [a, b]\) such that \(f(x) = 0\) using the one-dimensional root finding ITP method (Interpolate Truncate Project). Also see itp.

Usage

itp_root(
  f,
  a,
  b,
  k1 = 0.1,
  k2 = 2,
  n0 = 1,
  eps = 0.005,
  maxiter = 100,
  fa = NULL,
  fb = NULL,
  verbose = FALSE,
  ...
)

Arguments

f: The function to find the root of in terms of its first (one-dimensional) argument
a: The lower limit
b: The upper limit
k1: A tuning parameter
k2: Another tuning parameter
n0: Another tuning parameter
eps: Convergence tolerance
maxiter: Maximum number of iterations
fa: The value of f(a), if NULL then will be calculated
fb: The value of f(b), if NULL then will be calculated
verbose: Prints out information during iteration
...: Other arguments passed on to f

Value

A numeric vector of length 1, the root at the last iteration

References

I. F. D. Oliveira and R. H. C. Takahashi. 2020. An Enhancement of the Bisection Method Average Performance Preserving Minmax Optimality. ACM Trans. Math. Softw. 47, 1, Article 5 (March 2021), 24 pages. https://doi.org/10.1145/3423597

Examples

fpoly <- function(x) x^3 - x - 2 ## example from the ITP_method wikipedia entry
itp_root(fpoly, 1, 2, eps = .0001, verbose = TRUE)
#> iteration:  0 candidate:  1.433333 , closest value:  -0.4886296 
#> iteration:  1 candidate:  1.527131 , closest value:  0.03433833 
#> iteration:  2 candidate:  1.520093 , closest value:  -0.007641477 
#> iteration:  3 candidate:  1.521379 , closest value:  -4.253635e-06 
#> iteration:  4 candidate:  1.521383 , closest value:  1.964979e-05 
#> [1] 1.521381