Data Fitting

Abstract

Often a set of data points has to be fitted by a continuous function, either to obtain approximate function values in between the data points or to describe a functional relationship between two or more variables by a smooth curve, i.e., to fit a certain model to the data. If uncertainties of the data are negligibly small, an exact fit is possible, for instance, with polynomials, spline functions, or trigonometric functions. If the uncertainties are considerable, a curve has to be constructed that fits the data points approximately. The method of least square fit is introduced and the linear least square fit is discussed in detail. Numerical stability can be improved by applying the orthogonalization method instead of solving the normal equations directly. Another important method applies singular value decomposition to reduce redundancies and to extract the most important information from experimental data. An example for linear approximation is shown. A computer experiment demonstrates the least square fit for a typical physical problem.