In science and engineering, the data obtained from experiments usually contain a significant amount of random noise due to measurement errors. The purpose of curve fitting is to find a smooth curve that fits the data points on average. We usually require that this curve have a simple form with a low-order polynomial so that it does not reproduce the random errors of the data.
There is a distinction between interpolation and curve fitting. Interpolation, as discussed in the previous chapter, can be regarded as a special case of curve fitting in which the function must pass exactly through the data points. This implicitly ...