Interpolation

Abstract

Experiments usually produce a discrete set of data points. If additional data points are needed, for instance, to draw a continuous curve or to change the sampling frequency of audio or video signals, interpolation methods are necessary. But interpolation is also helpful to develop more sophisticated numerical methods for the calculation of numerical derivatives or integrals. Polynomial interpolation is discussed in large detail together with its drawbacks. The methods by Lagrange and Newton are discussed, as well as the Neville method, which allow efficient determination and evaluation of the interpolating polynomial. For interpolation over a larger range, larger number of data spline interpolation is very useful which does not show the oscillatory behavior characteristic of polynomial interpolation. In a computer experiment both these approaches are compared. Multivariate interpolation is a necessary tool to process multidimensional data sets, for instance, for image processing. A computer experiment compares bilinear interpolation and bicubic spline interpolation.