pkmon (version 1.1)

Delta: Discrete laplacian

Description

Computes the laplacians of a discrete function

Usage

Delta(k, L, p)

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 \(0,\ldots,L\).

Arguments

k

Maximum order of the laplacian

L

Support of the function

p

Discrete function represented as a vector

Author

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)