# fixedpoint: A function of the fixed point algorithm. In spuRs: Functions and Datasets for "Introduction to Scientific Programming and Simulation Using R"

## 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.

`newtonraphson`, `bisection`

## Examples

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

### Example output

```Loading required package: MASS
At iteration 1 value of x is: 1.144921
At iteration 2 value of x is: 1.374719
At iteration 3 value of x is: 1.287768
At iteration 4 value of x is: 1.317697
At iteration 5 value of x is: 1.307022
At iteration 6 value of x is: 1.310783
At iteration 7 value of x is: 1.309452
At iteration 8 value of x is: 1.309922
At iteration 9 value of x is: 1.309756
At iteration 10 value of x is: 1.309815
At iteration 11 value of x is: 1.309794
At iteration 12 value of x is: 1.309802
At iteration 13 value of x is: 1.309799
At iteration 14 value of x is: 1.3098
Algorithm converged
[1] 1.3098
```

spuRs documentation built on May 21, 2018, 9:03 a.m.