assist (version 3.1.9)

Polynomial: Calculate Reproducing Kernels for Polynomial Splines on [0, 1]

Description

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

Usage

linear(s, t=s)
cubic(s, t=s)
quintic(s, t=s)
septic(s, t=s)

Value

a matrix with the numbers of row and column equal to the lengths 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]).

Arguments

s

a vector of values in [0, 1], at which the kernels are evaluated.

t

an optional vector in [0, 1]. Default is the same as s.

Author

Chunlei Ke and Yuedong Wang

Details

The reproducing kernels implemented in these functions are based on Bernoulli functions with domain [0, 1].

References

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

See Also

ssr, linear2, cubic2, quintic2, septic2

Examples

if (FALSE) {
x<-seq(0, 1, len=10)
cubic(x)
}