# fixedPoint: Fixed Point Algorithm Infrastructure In wahani/saeRobustTools: Robust Small Area Estimation

## Description

A fixed-point function supplied by the user is iteratively evaluated. `addAverageDamp` can be used to add average damping to the function - this may have a positive effect on the speed of convergence.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```fixedPoint(fun, x0, convCrit) addAverageDamp(fun) addConstraintMin(fun, value) addConstraintMax(fun, value) convCritAbsolute(tolerance = 1e-06) convCritRelative(tolerance = 1e-06) addMaxIter(fun, maxIter) addCounter(fun) addHistory(fun) addStorage(fun) newtonRaphson(funList, ...) newtonRaphsonFunction(funList) ```

## Arguments

 `fun` the function to be evaluated in the algorithm `x0` starting value `convCrit` a function returning a logical scalar. Is called with two arguments; the first is the value from iteration n; the second is the value from iteration n-1 `value` (numeric) `tolerance` a numeric value > 0 `maxIter` maximum number of iterations `funList` (list) the functions to be evaluated in the algorithm. First element is typically the score function, second is the derivative of the score. `...` arguments passed to `fixedPoint`

## Details

`addAverageDamp` adds average damping to an arbitrary fixed point function.

`addConstraintMin` takes care that values are not below a minimum value.

`addConstraintMax` takes care that values are not larger than maximum value.

`convCritAbsolute` absolute difference as convergence criterion.

`convCritRelative` relative (to previous iteration) absolute difference as convergence criterion. If value is smaller than 1, absolute difference is used.

`addMaxIter` can be used to modify convergence criterion functions.

`addCounter` can be used to count the number of calls of a function.

`addHistory` can be used to save a history of results of a function. The history is stored as a matrix, so this works best if the return value of `fun` is numeric.

`addStorage` will add a storage to a function. The storage is a list in which each result is stored. The function will coerce the return value into a numeric.

`newtonRaphson` finds zeroes of a function. The user can supply the function and its first derivative. Note that the Newton Raphson Algorithm is a special case of a fixed point algorithm thus it is implemented using `fixedPoint` and is only a convenience.

## Examples

 ```1 2 3 4``` ```## Not run: vignette("fixedPoint", "saeRobust") ## End(Not run) ```

wahani/saeRobustTools documentation built on May 3, 2019, 8:09 p.m.