ABSTRACT
Problems requiring interpolation between individual data points occur frequently in science and engineering. The basis of all interpolation algorithms is the fitting of some type of curve or function to a subset of the tabular data; linear interpolation uses a straight line. Interpolation algorithms differ in the form of their interpolation functions. The method of undetermined coefficients is conceptually the simplest interpolation algorithm, and it illustrates many of the key points that hold for all interpolation schemes. The method of undetermined coefficients can be generalized to interpolation polynomials of any order. A finite-difference scheme can be used to develop an interpolation polynomial when the known values of the independent variable are equally spaced. The best interpolation method to use for any problem often depends on the details of the particular problem. The development of other methods is similar, but with an increased computational difficulty.
