Truncated power function

Contents

1 Definition
2 Relations
3 External links
4 References

Definition

The truncated power function^[1] with exponent $n$ is defined as

$x_%2B^n = \begin{cases} x^n &:\ x > 0 \\ 0 &:\ x \le 0. \end{cases}$

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

$x_%2B = \begin{cases} x &:\ x > 0 \\ 0 &:\ x \le 0. \end{cases}$

and interpret the exponent as conventional power.

Relations

Truncated power functions can be used for construction of B-Splines.
$x \mapsto x_%2B^0$ is the Heaviside function.
$\chi_{[a,b)}(x) = (b-x)_%2B^0 - (a-x)_%2B^0$ where $\chi$ is the indicator function.
Truncated power functions are refinable.

External links

Truncated Power Function on MathWorld

References

^ Massopust, Peter (2010). Interpolation and Approximation with Splines and Fractals. p. 46. ISBN 0195336542.