steffensens_method: Steffensen's method

In steventhornton/univariate: Roots of Univariate Functions

Description

Steffensen's method is an iterative root-finding method with quadratic convergence that does not use derivatives.

Usage

steffensens_method(f, x0, tol = 1e-08)

Arguments

f	Univariate function to find root of
x0	A point close to the root of f
tol	Tolerance for convergence.

Details

Steffensen's method finds the root of a univariate function f given an initial guess x_0 by the iteration:

x_{n + 1} = x_n - \frac{f(x_n)}{g(x_n)}

where

g(x_n) = \frac{f(x_n + f(x_n))}{f(x_n)} - 1

.

The algorithm terminates when:

• the algorithm exceeds 1000 iterations,

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

• the iterate (x_n) becomes non-finite, or

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

Value

A root of f near x0. If the algorithm does not converge, NA is returned.

Examples

steffensens_method(cos, 0)
steffensens_method(function(x) x ^ 3 - x - 2, 2)

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