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I'm working on a presentation in which I will be mentioning functions of the form

$$s_i(x) = \begin{cases}|x - x_i|, & |x - x_i| < 1 \\ 0, &\text{otherwise}\end{cases}$$

Basically, it's a single peak of a triangle wave, centered on some given value $x_i$. Does anyone know if there's a standard name for this sort of function?

For anyone who's interested, the use case is a program that computes the discrete values

$$f_i = \int s_i(x)f(x)\mathrm{d}x$$

for several functions, and then uses them for various numerical computations on the functions $f$. I'm not writing the program (that's been done), just analyzing it, and I'd like to be able to know what keywords to use to look up more information if/when I need it.

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It is often called the hat function. – yasmar Apr 10 '11 at 9:55
Also called a linear B-spline. – lhf Apr 10 '11 at 12:13
@yasmar: thanks, I would definitely accept that if it were an answer. – David Z Apr 11 '11 at 18:33
up vote 2 down vote accepted

It is often called the hat function. As lhf commented this is the basis function for linear B-splines.

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