On one method of approach reconstruction table form function to analytical form in domain point vicinity

Abstract

Mathematical model researches data is in numeric matrices or numeric data tables, as usual. Functions reconstruction when it is in table numeric data form is made on parameter mesh. Density parameter mesh reducing for reconstruction function problem will be urgency in spite of temporary computer speed operates.
Experimental data research allows obtaining the general algorithm for analytical form model reconstruction. The algorithm allow in high power reduce computer time waste for resultant function reconstruction but in point vicinity was proposed. So, instead of doing parameter mesh function values calculating, it is done in coordinate curves and as a result the resultant function number calculates are high reduced. The new sequence approximation method (SAM) allow to do analytical function form reconstruction (in univariable function product form) when it exist in table form in point vicinity. As experience is demonstrated, solutions of real tasks allow representing them in whole domain. In spite of the fact that the errors of the function representation raised up to domain boundary errors do not exceed 5-7%.. Thus influence parameter evaluating method consists of approximate solution reconstruction in form of exponent functions and its index exponent comparisons. Greater index value, stronger function parameter influence.
For testing the accuracy limits we make the reconstruction of some analytical form functions. Graphic dependencies are present.