Linear spline
= Linear spline
{title2=$s(t)=\sum_i c_i\max(1-|t-i|,0)$}
A <linear spline> is a continuous <piecewise linear function> on a specified <spline knot sequence>. For uniform integer <spline knots>, the hat basis in the displayed representation interpolates the data $s(i)=c_i$. The <derivative> is constant on each open span and can jump at a knot. Coinciding neighboring slopes remove a particular jump, but generic data give only $C^0$ regularity.