# A function of the fixed point algorithm.

### Description

Applies the fixed point algorithm to find x such that ftn(x) == x.

### Usage

1 | ```
fixedpoint(ftn, x0, tol = 1e-09, max.iter = 100)
``` |

### Arguments

`ftn` |
the function. |

`x0` |
is the initial guess at the fixed point. |

`tol` |
distance of successive iterations at which algorithm terminates. |

`max.iter` |
maximum number of iterations. |

### Details

We assume that `ftn` is a function of a single variable.

### Value

Returns the value of x at which ftn(x) == x. If the function fails to
converge within `max.iter` iterations, returns `NULL`.

### References

Jones, O.D., R. Maillardet, and A.P. Robinson. 2009. An Introduction to Scientific Programming and Simulation, Using R. Chapman And Hall/CRC.

### See Also

`newtonraphson`

, `bisection`

### Examples

1 2 | ```
ftn1 <- function(x) return(exp(exp(-x)))
fixedpoint(ftn1, 2, tol = 1e-6)
``` |

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