R: Aitken' Method

aitken {pracma} | 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.

### See Also

`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

[Package pracma version 2.0.4 Index]