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  4. Approximation of functions of root mean square errors of land parcels areas to determine their allowable value

Approximation of functions of root mean square errors of land parcels areas to determine their allowable value

ISTCGCAP.
2014;
Volume 79, Number 79
: pp. 54 - 67
Received: January 17, 2014
Accepted: March 24, 2014
Authors:
  1. V. V. Riabchii
  2. M. Trehub
1
Department of Geodesy, Lviv PolytechnicNational University, State Higher Educational Institution “National Mining University”
2
State Higher Educational Institution “National Mining University”; Kyiv National University of Construction and Architecture

The purpose of this article is the research of results of approximation of functions of calculation of the meansquare errors of land parcels areas to determine such approximation function, which would allow most accurately calculate the permissible values of mean square errors depending on the size and elongation of land parcel. Methods. To meet the goal an approximation of functions by the method of least squares was performed. Two functions were used for approximation – the natural logarithm and power, as well as the evaluation of the accuracy was done. The study found that the mean square error of the areas of land parcels are well described by these two functions, that is confirmed by the obtained values of the coefficient of determination which are close to unity. Scientific novelty of this study lies in the fact that the established mathematical dependences allow differentially depending on the area of land parcel and elongation coefficient to establish allowable mean square error of the determination of areas of land parcels with size from 0.1 to 100 ha. Both functions provide almost equal results. The practical significance. The corresponding conclusions and suggestions on developed mathematical models (formulas) that can be used by geodetic and land management organizations, territorial divisions of the State Agency of Land Resources of Ukraine and regional centers of the State Land Cadastre of Ukraine, their supervisory authorities to quickly identify and verify the values of the land parcels areas errors, as well as in the educational process.

approximation
estimation accuracy
root mean square error
land parcel
land parcel area
the elongation coefficient of land parcel
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