Interpolation with Spline Functions

Many scientific and engineering phenomena being measured undergo a transition from one physical domain to another. Data obtained from these measurements are better represented by a set of piecewise continuous curves rather than by a single curve. One of the difficulties with polynomial interpolation is that in some cases the oscillatory nature of high-degree polynomials can induce large fluctuations over the entire range when approximating a set of data points. One way of solving this problem is to divide the interval into a set of subintervals and construct a lowerdegree approximating polynomial on each subinterval. This type of approximation is called piecewise polynomial interpolation.