Truncated power function

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

[edit] Definition

Given a function f the truncated power function is defined as

$f_+^n := \left\{\begin{matrix} f^n &\mbox{if}\ f \ge 0 \\ 0 &\mbox{if}\ f < 0 \end{matrix}\right.$

$\chi_{(a,b]}(x) = (b-x)_+^0 - (a-x)_+^0$