rootfinding_and_minimisation: Root-Finding and Minimisation Functions

Description

Functions for root-finding and minimisation using various algorithms.

Usage

bisect(
  f,
  lower,
  upper,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)
bracket_and_solve_root(
  f,
  guess,
  factor,
  rising,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)
toms748_solve(
  f,
  lower,
  upper,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)
newton_raphson_iterate(
  f,
  guess,
  lower,
  upper,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)
halley_iterate(
  f,
  guess,
  lower,
  upper,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)
schroder_iterate(
  f,
  guess,
  lower,
  upper,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)
brent_find_minima(
  f,
  lower,
  upper,
  digits = .Machine$double.digits,
  max_iter = .Machine$integer.max
)

Value

A list containing the root or minimum value, the value of the function at that point, and the number of iterations performed.

Arguments

f: A function to find the root of or to minimise. It should take and return a single numeric value for root-finding, or a numeric vector for minimisation.
lower: The lower bound of the interval to search for the root or minimum.
upper: The upper bound of the interval to search for the root or minimum.
digits: The number of significant digits to which the root or minimum should be found. Defaults to double precision.
max_iter: The maximum number of iterations to perform. Defaults to the maximum integer value.
guess: A numeric value that is a guess for the root or minimum.
factor: Size of steps to take when searching for the root.
rising: If TRUE, the function is assumed to be rising, otherwise it is assumed to be falling.

Details

This package provides a set of functions for finding roots of equations and minimising functions using different numerical methods. The methods include bisection, bracket and solve, TOMS 748, Newton-Raphson, Halley's method, Schroder's method, and Brent's method. It also includes functions for finding roots of polynomials (quadratic, cubic, quartic) and computing minima.

Examples

Run this code

f <- function(x) x^2 - 2
bisect(f, lower = 0, upper = 2)
bracket_and_solve_root(f, guess = 1, factor = 0.1, rising = TRUE)
toms748_solve(f, lower = 0, upper = 2)
f <- function(x) c(x^2 - 2, 2 * x)
newton_raphson_iterate(f, guess = 1, lower = 0, upper = 2)
f <- function(x) c(x^2 - 2, 2 * x, 2)
halley_iterate(f, guess = 1, lower = 0, upper = 2)
schroder_iterate(f, guess = 1, lower = 0, upper = 2)
f <- function(x) (x - 2)^2 + 1
brent_find_minima(f, lower = 0, upper = 4)