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. Usually a model function is used which depends on a set of parameters which have to be determined such that the overall error is minimized, which in most practical cases is measured by the mean square difference. The optimal parameters are determined by solving the system of normal equations. If the model function depends linearly on the parameters, orthogonalization offers a numerically more stable method. The dimensionality of a data matrix can be reduced with the help of singular value decomposition, which allows to approximate a matrix by another matrix of lower rank and is also useful for linear regression, especially if the columns of the data matrix are linearly dependent.
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