Approximation

Abstract

Data, either computed or gathered, is imperfect and/or incomplete, and having a handful of methods to display, analyze, and compress it is important. We consider three introductory methods that should be known by computational scientists. The first approximation is the method of least squares, which is a technique to optimize a particular functional form to a collection of data. If data is assumed to be stochastic, i.e. drawn from a random process, then the method of least squares supports the substantial statistical study known as linear regression. The second approximation is that of cubic splines, which creates a smooth curve to match data. The third approximation is principal component analysis, which compresses data to preserve statistical characteristics.