R: Computes the semi-kernel of Duchon splines

DuchonQ {ibr}

R Documentation

Computes the semi-kernel of Duchon splines

Description

The function DuchonQ computes the semi-kernel of Duchon splines. This function is not intended to be used directly.

Usage

DuchonQ(x,xk,m=2,s=0,symmetric=TRUE)

Arguments

`x`	A numeric matrix of explanatory variables, with n rows and p columns.
`xk`	A numeric matrix of explanatory variables, with nk rows and p columns.
`m`	Order of derivatives.
`s`	Exponent for the weight function.
`symmetric`	Boolean: if `TRUE` only `x` is used and it computes the semi-kernel at observations of `x` (it should give the same result as `DuchonQ(x,xk,m,s,FALSE)`).

Value

The semi-kernel evaluated.

Author(s)

Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober.

References

Duchon, J. (1977) Splines minimizing rotation-invariant semi-norms in Solobev spaces. in W. Shemp and K. Zeller (eds) Construction theory of functions of several variables, 85-100, Springer, Berlin.