assist (version 2.0)

Polynomial2: Calculate Reproducing Kernels for Polynomial Splines on [0, T]

Description

Return a matrix evaluating reproducing kernels for polynomial splines at observed points.

Usage

linear2(s, t=s)
cubic2(s, t=s)
quintic2(s, t=s)
septic2(s, t=s)

Arguments

s

a vector of non-negative values, at which the kernels are evaluated.

t

an optional non-negative vector. Default is the same as s.

Value

• a matrix with the numbers of row and column equal to the length of s and t respectively. The [i, j] element is the reproducing kernel of linear, cubic, quintic, or septic spline evaluated at (s[i], t[j]).

Details

The reproducing kernels implemented in these functions are based on Green functions. The domain is [0, T], where T is a given positive number.

References

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.

See Also

ssr, linear, cubic, quintic, septic

Examples

x<- seq(0, 5, len=10)
linear2(x)