Abstract
A new method for smooth interpolation and approximation of data is introduced. The method is based on choosing the smoothest analytical curve that approximates the data points. The method allows for the inclusion of additional information, such as uncertainties in the data and other constraints given by the general phenomenology of the experiment or theory. The novelty in the method, as well as its most efficient feature, is in its ability to obtain a good approximation, not only of the data points, but also of their first and higher derivatives. The method is applied to several examples. Among them we include function approximations and several physical experiments, such as heat capacity measurement and Mössbauer spectrum. Another interesting example that is treated involves a calibration of GaAs resistance thermometer. The method is extended to multidimensional spaces, and can also be applied to the calculation of numerical derivatives and integrals of data points.
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