Interpolation versus Curve Fitting

• Given a set of data
  $y_i=f(x_i)      i=1,\ldots,n$
  obtained from an experiment or from some calculation.
• In curve fitting, the approximating function passes near the data points, but (usually) not exactly through them. There is some uncertainty in the data.
• In interpolation, process inherently assumes that the data have no uncertainty. The interpolation function passes exactly through each of the known data points.

• Figure 5.1 shows a plot of some hypothetical experimental data, a curve fit function and interpolating with piecewise-linear function.

Figure 5.1: A curve fit function passes near the data points. An interpolating function passes exactly through the data points.