Piecewise Interpolation

Definition

Although an appropriate choice of a basis function can mitigate difficulties with interpolation by a polynomial of a high degree, fitting a single polynomial to a large number of data points is still likely to yield unsatisfactory oscillating behaviour in the interpolant.

The main advantage of piecewise polynomial interpolation is that you can fit many smaller degree polynomials to a large number of data points.

Although piecewise polynomial interpolation eliminates the problems of excessive oscillation and nonconvergence, it sacrifices smoothness of the interpolating function.

Hermite Cubic Interpolation is able to allow for smoothness.