Metric analysis, properties and applications as a tool for interpolation

Abstract

One of the primary goals of data processing is the problem of interpolation of the values of investigated function. Different methods and schemes for the solving various interpolation problems are developed and in use [1-3]. The schemes of metric analysis for restoration of function of one and many variables are also in use [4-9]. The new approach for one dimensional and multidimensional interpolation, named by authors "metric analysis", and the algorithms based on this approach are offered. It is shown that the metric analysis interpolates multidimensional functions with high accuracy, even in the case of a small number of points in which values of the function are defined (interpolation knots).

Mathematical model comparing of the multi-level economics systems

“…To solve the problems of the forecasting of the particular indicators, the methods of the metric analysis [12][13][14][15] ,..., 1 , ,.., 1 ,   are the particular first-level indicators that are included in the j-th integral index of the second level, and in the j-th integral index of the third level, respectively (see [1,2]). …”

“…To solve the problems of the forecasting of the particular first-level indicators, the methods of the metric analysis [12][13][14][15] can be used.…”

Metric analysis, properties and applications as a tool for forecasting

“…For extrapolation on the uniform grid it is used the nonlinear autoregressive scheme which allows to solve the problem of extrapolation by means of multidimensional interpolation. The multidimensional interpolation is based on metric analysis [5,6,7,9].…”

Metric analysis properties and applications as a tool for smoothing

“…The values of function ( ⃗⃗⃗ ) are known with errors at points ⃗⃗⃗ . Assume the matrix of metric uncertainty W is not singular [11]. For any point ⃗⃗⃗⃗ we are looking for the smoothing value Y* in representation ∑ ( ⃗ ) (2) where the vector of weights is the solution of the following problem on a minimum of the total uncertainty:…”