I sense a tendency here to see interpolation
as just a particular case of imputing missing
values, but I think that can be misleading.
The particularities of interpolation are more important
than the similarities to other kinds of imputation.
Interpolation historically within mathematics
and science -- and the history covers many
centuries -- covers single-valued responses
for a grid of values of time or some other controlling
variable(s). For some of that grid, we may lack response values
and therefore might wish to interpolate. This
will only work well with small gaps and smooth
behaviour.
