    Next: Piecewise linear interpolation Up: Piecewise Polynomial Interpolation. Splines. Previous: Piecewise Polynomial Interpolation. Splines.   Contents

# The Piecewise Interpolation Problem

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

are polynomial of the degree wanted. Since we want to be continuous we require that    Next: Piecewise linear interpolation Up: Piecewise Polynomial Interpolation. Splines. Previous: Piecewise Polynomial Interpolation. Splines.   Contents