I-spline


In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function.
[Image:Ispline order3.svg|thumb|325px|An I-spline family of order three with four interior knots.]

Definition

A family of I-spline functions of degree k with n free parameters is defined in terms of the M-splines Mi
where L is the lower limit of the domain of the splines.
Since M-splines are non-negative, I-splines are monotonically non-decreasing.

Computation

Let j be the index such that tj ≤ x < tj+1. Then Ii is zero if i > j, and equals one if j − k + 1 > i. Otherwise,

Applications

I-splines can be used as basis splines for regression analysis and data [transformation (statistics)|data transformation] when monotonicity is desired.