`Given the data points for ,
we want to find continuous function that ``passes through''
all the data points.
`

`One possibility is to compute a degree
polynomial that passes through each of the the data points.
Such a polynomial exists and can be uniquely determined; fitting
a single polynomial to a large number of data points can lead to insatisfactory
results.
We have seen however that between the interpolation points the
polynomial oscillates, and these oscillations grow larger for
higher order polynmials.
`

`We want to use a low order polynomial that interpolates several
points in the data set. On each subinterval we will have a different
such polynomial; thus we use piecewise polynomial interpolation.
`

`For our data set the interpolating function is
`