Metric analysis and applications

A new approach to the interpolation of functions of one or several variables and to the time series forecasting (extrapolation) as well as some schemes and algorithms based on it are proposed. This approach is called the metric analysis. The metric analysis shows a high accuracy in interpolating the functions of several variables, even in the case of a comparatively small number of points with known function values. It is found that the metric analysis allows one to extrapolate and forecast the values of functions of a wider class than the known singular spectrum analysis.