ANALYSIS OF THE ACCURACY OF THE SOLUTION OF THE INTEGRAL EQUATION OF THE INTERPRETATION PROBLEM

Authors

Majid Malikovich Karimov, Tashkent State Technical University Address: 2 Universitetskaya st., 100095, Tashkent city, Republic of Uzbekistan.Follow
Mirhusan Mirazizovich Sagatov, Tashkent State Technical University Address: 2 Universitetskaya st., 100095, Tashkent city, Republic of Uzbekistan. E – mail: informtgtu@mail.ru.Follow

Abstract

Intensive development and expansion of the field of application of modern observation systems are largely determined by the improvement of methods and means of interpreting the primary results recorded by the system. The high quality of the results of solving interpretation problems is achieved by improving such indicators as accuracy, resolution, speed. In the general case, the influence of the observation system on the result is naturally described by an integral equation, which is a general integral mathematical model for the problems of interpreting the results of observations. In the presented article, it is proposed to improve the accuracy of interpretation of the results of observations using a smoothing spline approximation of the values of the scanned function. Also estimates of the error of the spline approximation of the scanned function and the error of solving the integral equation and choosing the degree of the spline are presented.

First Page

67

Last Page

76

References

1. Verlan, A.F., Sagatov, M. V. (2021). Inverse problems of the dynamics of observation interpretation systems. J. Phys.: Conf. Ser. 2131 032109, [Online]. DOI: 10.1088/1742-6596/2131/3/032109.
2. Mosentsova, L.V. (2009). Primeneniye metodov vychislitel'nykh eksperimentov i obobshchennogo printsipa nevyazki dlya resheniya zadachi povysheniya razreshayushchey sposobnosti antenny [Application of methods of computational experiments and the generalized residual principle for solving the problem of increasing the resolution of an antenna]. Zbírnik naukovikh prats' Ínstitutu problem modelyuvannya v yenergetitsí ím. G.Ê. Pukhova NAN Ukraí̈ni. — K.: ÍPME ím. G.Ê. Pukhova NAN Ukraí̈ni, 52, 18-25.
3. Pyt'yev, YU.P., Chulichkov, A.I. (1983). Pribor + EVM = novyye vozmozhnosti [Device + computer = new opportunities]. M.: Znaniye, 119 p. (in Russian).
4. Verlan, A.F., Sizikov, B.C. (1986). Integral'nyye uravneniya: metody, algoritmy, programmy [Integral Equations: Methods, Algorithms, Programs]. K.: Naukova dumka, 544 p. (in Russian).
5. Verlan, A.F., Goroshko, I.O., Karpenko, Ye.YU., Korolev, V.YU., Mosentsova, L.V. (2011). Metody i algoritmy vosstanovleniya signalov i izobrazheniy [Methods and algorithms for signal and image recovery]. K.: Naukova dumka, 368 p. (in Russian).
6. Godlevskiy, V.S., Godlevskiy, V.V.(2020). Voprosy tochnosti pri obrabotke signalov [Precision Issues in Signal Processing]. Kiyev: Al'fa reklama, 407 p. (in Russian).
7. Khímích, O.M., Níkolaêvs'ka, O.A., Chistyakova, T.V. (2017). Pro deyakí sposobi pídvishchennya tochností komp’yuternikh obchislen' Matematichne ta komp’yuterne modelyuvannya [About methods for improving the accuracy of computer calculations Mathematical and computer modeling]. Seríya: Fíziko-matematichní nauki. 15, 249-254.
8. Verlan, D.A. (2014). Metod vyrozhdennykh yader pri chislennoy realizatsii integral'nykh dinamicheskikh modeley [The Method of Created Kernels in the Numerical Implementation of Integral Dynamic Models]. Elektronnoye modelirovaniye. 36(3). 41-57.
9. Verlan, A.F., Verlan, A.A., Polozhayenko, S.A. (2017). Algoritmizatsiya metodov tochnostnoy parametricheskoy reduktsii matematicheskikh modeley [Algorithmization of Methods for Precision Parametric Reduction of Mathematical Models]. Ínformatika ta matematichní metodi v modelyuvanní, 7(1-2). 7-18.
10. Collatz, L., Krabs, W. (1973). Approximationstheorie: Tschebyscheffsche Approximation mit Anwendungen, Teubner, Stuttgart.
11. Malachivskyy, P.S., Pizyur, Y.V., Malachivskyi, R.P., Ukhanska, O.M. (2020). Chebyshev approximation of functions of several variables. Cybernetics and Systems Analysis, 56(1), 118-125.
12. Berdyshev, V.I., Subbotin, YU.N. (1979). Chislennyye metody priblizheniya funktsiy [Numerical Methods for Function Approximation]. Sverdlovsk: Sredne-Ural'skoye kn. izd-vo, 120 p.
13. Grebennikov, A.I. (1983). Metod splaynov i resheniye nekorrektnykh zadach teorii priblizheniy [The spline method and the solution of ill-posed problems in approximation theory]. M.: Izd-vo Mosk. un-ta, 208 p. (in Russian).
14. Zav'yalov, YU.C., Kvasov, B.I, Miroshnichenko, V.L. (1980). Metody splayn funktsiy [Spline Function Methods]. M.: Nauka, 350 p. (in Russian).
15. Verlan, D.A., Chevs'ka, K.S. (2013). Otsínka pokhibok rozv’yazannya íntegral'nikh rívnyan' Vol'terri ÍÍ rodu zasobami íntegral'nikh nerívnostey. Matematichne ta komp'yuterne modelyuvannya. Ser. : Tekhníchní nauki. 9. 23-33.

Recommended Citation

Karimov, Majid Malikovich and Sagatov, Mirhusan Mirazizovich (2023) "ANALYSIS OF THE ACCURACY OF THE SOLUTION OF THE INTEGRAL EQUATION OF THE INTERPRETATION PROBLEM," Chemical Technology, Control and Management: Vol. 2023: Iss. 1, Article 9.
DOI: https://doi.org/10.59048/2181-1105.1445