ABOUT SPECIAL CASES OF LAGRANGIAN INTERSTRIPATION OF APPROXIMATIONS OF FUNCTIONS OF TWO VARIABLES
DOI:
https://doi.org/10.15588/1607-3274-2025-4-5Keywords:
numerical methods, mathematical modeling, information operators, interlination, interstripationAbstract
Context. The problem of approximating the values of continuous functions of two variables based on known information about them on stripes, the boundaries of which are parallel to the coordinate axes, is considered. The object of the study is the process of approximating the values of functions based on incomplete information about them, which is given on the system of stripes.
Objective. The goal of the work is the review of information operators of Lagrangian interstripation and features of the construction of information approximation operators for some cases of the mutual arrangement of stripes in some region, which allow to significantly simplify the calculation of approximate values of the function in unknown subregions of the region.
Method. Methods for approximating the values of continuous functions of two variables with incomplete information about them on some limited area are proposed. Information about the function is known only on a system of stripes limited by straight lines parallel to the coordinate axes. A method for approximating the values of continuous functions of two variables, information about which is known on two stripes, as a result of union of which only some rectangular subregion remains unknown in the region, is proposed. A method for approximating the values of continuous functions of two variables, information about which is known on three stripes, as a result of union of which only some rectangular subregion remains unknown in the region, is proposed. A method for approximating the values of continuous functions of two variables, information about which is known on four stripes, as a result of union of which only some rectangular subregion remains unknown in the region, is proposed. A method for approximating the values of continuous functions of two variables, the information about which is known on two stripes, as a result of union of which four rectangular subregions remain unknown in the region, is proposed. For all the considered cases, approximation operators are given that allow calculating the approximate form of the function in the unknown subregions in the analytical form.
Results. The information operators of Lagrangian interstripation are implemented programmatically and investigated in problems of approximating the values of functions of two variables from known information about them on the systems of stripes.
Conclusions. The experiments confirmed the accuracy of approximation of the values of continuous functions of two variables
of the proposed information interstripation operators for different systems of stripes. Approximation operators are given for special cases of the location of stripes in the region, the difference of which from the information interstripation operators of the general form lies in the significant simplification of the approximation operators without losing the accuracy of the approximation with a smaller number of arithmetic operations, which can be a decisive factor in some cases. Prospects for further research lie in the application of the proposed information operators in the problems of digital image processing, seismic mineral exploration data and remote sensing data etc.
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