kernel4 {rmargint}

Order 4 kernel

Description

This function evaluates a kernel of order 4.

Usage

kernel4(x)

Arguments

x

A vector of real numbers.

Details

This function evaluates a kernel of order 4. A kernel L is a kernel of order 4 if it integrates 1, the integrals of u^j L(u) are 0 for 1 <= j < 4 (j integer) and the integral of u^4 L(u) is different from 0.

Value

A vector of the same length as x where each entry is ( 15/32 ) * ( 1 - x^2 ) * ( 3 - 7 * x^2 ) if abs(x) < 1 and 0 otherwise.

Author(s)

Alejandra Martinez, [e-mail], Matias Salibian-Barrera

Examples

x <- seq(-2,2,length=10)
kernel4(x)