bisection_method: Bisection method

In steventhornton/univariate: Roots of Univariate Functions

Description

The bisection method is an iterative root-finding method with linear convergence that does not use derivatives.

Usage

bisection_method(f, x0, x1, tol = 1e-08)

Arguments

f	Univariate function to find root of
x0	A point
x1	A point larger than x0
tol	Tolerance for convergence.

Details

The bisection method finds the root of a univariate function f given two initial guesses x_0 and x_1 where x_0 < x_1 and sign(f(x_0)) = -sign(f(x_1)) by sequentially bisecting the interval (x_2 = (x_0 + x_1) / 2).

Convergence is guaranteed as long as f is continuous in the interval [x_0, x_1] and f(x_0) and f(x_1) have opposite signs

The algorithm terminates when:

• the algorithm exceeds 1000 iterations,

• the value of f is non-finite for an iterate (x_n),

• the algorithm converges and |f(x_{n}) - f(x_{n + 1})| < tol.

Value

A root of f. If the algorithm does not converge, NA is returned.

Examples

bisection_method(cos, 0, pi)
bisection_method(function(x) x ^ 3 - x - 2, 1, 2)

steventhornton/univariate documentation built on June 5, 2020, 2:37 p.m.