Piecewise Polynomial Interpolation

When data points are spread over a wide range, interpolating polynomials of very high degree may be needed to satisfy the required accuracy.

An alternative strategy is to subdivide the interval in smaller intervals and use lower degree polynomials in each of these subintervals. This approach is called piecewise polynomial interpolation . Let us illustrate the idea with a few examples:

piecewise linear approximation

cubic spline interpolation