A Review of Metric Analysis Applications to the Problems of Interpolating, Filtering and Predicting the Values of Onevariable and Multivariable Functions

Abstract

At present, metric analysis schemes are developed to solve the problems of interpolation, smoothing, extrapolation of multivariable functions and their use for many applied problems [1, 2, 3, 4, 5, 6, 7]. In contrast to classical methods and schemes and a majority of other ones [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23], the metric analysis, like artificial neuron networks, allows reconstructing the studied function values at each specified point of the definition domain separately. The individual position of this point with respect to the ones, where the values of the function are defined, is taken into account. Here we present a review of the published papers on the metric analysis used to solve the above problems, including those under the conditions of uncertainty of the defined values of the studied function. We present recommendations on using the metric analysis schemes and demonstrate the efficiency of the metric analysis methods and schemes.