# fhappx: Floater-Hormann interpolation on a grid In chebpol: Multivariate Interpolation

## Description

The Floater-Hormann interpolation.

## Usage

 `1` ```fhappx(...) ```

## Arguments

 `...` Further arguments to the function, if `is.function(val)`. `val` array or function. Function values on a grid, or the function itself. If it is the values, the `dim`-attribute must be appropriately set. `grid` list. Each element is a vector of ordered grid-points for a dimension. These need not be Chebyshev-knots, nor evenly spaced. `d` integer. The degree of the blending polynomial.

## Details

A call `fun <- fhappx(val,grid)` creates a Floater-Hormann rational interpolant function `fun` on the grid. The degree of the blending polynomial,`d`, can be a vector, different for each grid-dimension. In theory, `d` can be any integer between 0 and the grid-dimension, a higher `d` yields a smoother fit. However, increasing `d` leads to exponential growth in rounding errors, so there is a tradeoff somewhere which depends on the analyticity of the function, and not in an obvious way. Current recommendations is to start low, at 3 or 4, and increase if necessary.

If `val` is a function it will be evaluated on the grid.

## Value

A `function(x)` defined on the hypercube, approximating the given function. The interpolant function uses the barycentric Floater-Hormann interpolation.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```## Not run: ## evenly spaced grid-points su <- seq(0,1,length.out=10) ## irregularly spaced grid-points s <- su^3 ## create approximation on the irregularly spaced grid fh1 <- fhappx(exp,grid=list(s)) ## test it fh1(su) - exp(su) ## two dimensional approximation f <- function(x) exp(sum(x^2)) grid <- list(s,su) fh2 <- fhappx(evalongrid(f,grid=grid),grid=grid) # an equivalent would be fh2 <- fhappx(f,grid) a <- runif(2); fh2(a); f(a) ## End(Not run) ```

### Example output

```Warning message:
'fhappx' is deprecated.
See help("Deprecated") and help("chebpol-deprecated").
[1]  0.0000000000  0.0006230181 -0.0017954460  0.0023154134  0.0020602738
[6] -0.0065596337 -0.0038716284  0.0098554452  0.0172406074  0.0000000000
Warning message:
'fhappx' is deprecated.