Article in Press
This article is currently in the Just Accepted phase. The final published version may have formatting changes or additional corrections.
Abstract
A new method of approximation by linear functions of random points specified in the Cartesian coordinate system is proposed and tested. The coefficients of the equation are determined from the condition of the minimum sum of the squares of the distances to the given points.
In contrast to the classical method of approximation by linear functions, the proposed method does not lead to the uniqueness of the solution.
A brief summary of the theory of the new method and its application is given. In particular, the following problems are considered: approximation of a random numerical field; interpolation of experimental data; analysis of the variance of the results of experiments; optimal placement of machine-building equipment; forecast of the number of products. The results of the calculations showed the high efficiency of the proposed method for solving practical problems.
