Truncated power function
From HandWiki
In mathematics, the truncated power function[1] with exponent [math]\displaystyle{ n }[/math] is defined as
- [math]\displaystyle{ x_+^n = \begin{cases} x^n &:\ x \gt 0 \\ 0 &:\ x \le 0. \end{cases} }[/math]
In particular,
- [math]\displaystyle{ x_+ = \begin{cases} x &:\ x \gt 0 \\ 0 &:\ x \le 0. \end{cases} }[/math]
and interpret the exponent as conventional power.
Relations
- Truncated power functions can be used for construction of B-splines.
- [math]\displaystyle{ x \mapsto x_+^0 }[/math] is the Heaviside function.
- [math]\displaystyle{ \chi_{[a,b)}(x) = (b-x)_+^0 - (a-x)_+^0 }[/math] where [math]\displaystyle{ \chi }[/math] is the indicator function.
- Truncated power functions are refinable.
See also
External links
References
- ↑ Massopust, Peter (2010). Interpolation and Approximation with Splines and Fractals. Oxford University Press, USA. p. 46. ISBN 0-19-533654-2.
 |  |
