I've seen some references to antilimits in the numerical analysis literature, but no definition of the term. The impression I get is that in specific contexts where every sequence $x_0,x_1,x_2,\dots$ under consideration has a unique extrapolation backward to $x_{-1},x_{-2},x_{-3},\dots$, and this extrapolated sequence converges to a limit $L$, we say that $L$ is an antilimit of the original sequence.

Is that all there is to it?

Can anyone provide information on contexts in which the concept of antilimits is useful?