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Smooth interpolation of large sets of scattered data

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Abstract

Methods for solving the following data-fitting problems are discussed: given the data (xi, yi, fi),i = 1,…,N construct a smooth bivariate function S with the property that S(xi, yi) = fii = 1,…,N. Because the desire to fit this type of data is encountered frequently in many areas of scientific applications, an investigation of the available methods for solving this problem was undertaken. Several aspects, such as computational efficiency, fitting characteristics and ease of implementation, were analysed and compared. Within the context of a general-purpose method for large sets of data, two of these methods emerged as being generally superior to the others. It is the purpose of this paper to describe these two methods and present examples illustrating their use and application.

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