Delta {pkmon}

Discrete laplacian

Description

Computes the laplacians of a discrete function

Usage

Delta(k, L, p)

Arguments

k

Maximum order of the laplacian

L

Support of the function

p

Discrete function represented as a vector

Value

Returns a matrix with the laplacians (-1)^j\Delta^j (p(l)) of vector p for j in 1,\ldots,k and l in 0,\ldots,L.

Author(s)

Jade Giguelay

References

Knopp K. (1925), <DOI:10.1007/BF01479598> Mehrfach monotone Zahlenfolgen, Mathematische Zeitschrift, 22, 75–85

Giguelay, J., (2016), Estimation of a discrete distribution under k-monotony constraint, in revision, (arXiv:1608.06541)

See Also

kKnot

Examples

p=dSpline(k=3, supp=20)
M=Delta(3, 20, p)