Truncated power function: Difference between revisions

Revision as of 09:27, 14 September 2011

Revision as of 09:42, 14 September 2011

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{{references|date=October 2009}}

{{expert-subject|Mathematics|date=October 2009}}

In the [[mathematical]] subfield of [[numerical analysis]] the '''truncated power function''' is a generalization of the [[indicator function]].

==Definition==

Given a function ''f'' theThe '''truncated power function'''<ref>{{cite is defined asbook

|title=Interpolation and Approximation with Splines and Fractals

|first=Peter|last=Massopust

|publisher: Oxford University Press, USA

|year=2010

|isbn=0195336542

|page=46

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

:<math>f_x_+^n :=

\left\{\begin{matrixcases}

fx^n &\mbox{if}:\ fx \ge 0 \\

0 &\mbox{if}:\ fx < 0.

\end{matrixcases}\right.

</math>

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

:<math>x_+ =

\begin{cases}

x &:\ x \ge 0 \\

0 &:\ x < 0.

\end{cases}

</math>

and interpret the exponent as conventional [[power function|power]].

==Notes==

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*[http://mathworld.wolfram.com/TruncatedPowerFunction.html Truncated Power Function on MathWorld]

==References==

[[Category:Numerical analysis]]

<references/>

[[Category:Numerical analysis]]

{{math-stub}}