# aitken: Aitken' Method In pracma: Practical Numerical Math Functions

 aitken R Documentation

## Aitken' Method

### Description

Aitken's acceleration method.

### Usage

``````aitken(f, x0, nmax = 12, tol = 1e-8, ...)
``````

### Arguments

 `f` Function with a fixpoint. `x0` Starting value. `nmax` Maximum number of iterations. `tol` Relative tolerance. `...` Additional variables passed to f.

### Details

Aitken's acceleration method, or delta-squared process, is used for accelerating the rate of convergence of a sequence (from linear to quadratic), here applied to the fixed point iteration scheme of a function.

### Value

The fixpoint (as found so far).

### Note

Sometimes used to accerate Newton-Raphson (Steffensen's method).

### References

Quarteroni, A., and F. Saleri (2006). Scientific Computing with Matlab and Octave. Second Edition, Springer-Verlag, Berlin Heidelberg.

`lambertWp`

### Examples

``````# Find a zero of    f(x) = cos(x) - x*exp(x)
# as fixpoint of  phi(x) = x + (cos(x) - x*exp(x))/2
phi <- function(x) x + (cos(x) - x*exp(x))/2
aitken(phi, 0)  #=> 0.5177574
``````

pracma documentation built on Nov. 10, 2023, 1:14 a.m.