Truncated power function: Difference between revisions

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TheIn mathematics, the '''truncated power function'''<ref>{{cite book

{{lead missing}}

==Definition==

The '''truncated power function'''<ref>{{cite book

|title=Interpolation and Approximation with Splines and Fractals

|first=Peter|last=Massopust

|publisher:= Oxford University Press, USA

|year=2010

|isbn=0195336542978-0-19-533654-2

|page=46

}}</ref> with exponent <math>n</math> is defined as

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</math>

In particular,

Alternatively, you may consider the subscript plus as an individual function with

:<math>x_+ =

\begin{cases}

Line 27 ⟶ 25:

==Relations==

* Truncated power functions can be used for construction of [[B-Splinespline]]s.

* <math>x \mapsto x_+^0</math> is the [[Heaviside function]].

* <math>\chi_{[a,b)}(x) = (b-x)_+^0 - (a-x)_+^0</math> where <math>\chi</math> is the [[indicator function]].

* Truncated power functions are [[refinable function|refinable]].

== See also ==

* [[Macaulay brackets]]

==External links==