BSU bulletin
Mathematics, Informatics
LoginРУСENG

BSU bulletin. Mathematics, Informatics

Bibliographic description:
Serebryansky S. М.
,
Tyrsin A. N.
IMPROVING ТНЕ ACCURACY OF SOLVING INVERSE PROBLEMS WIТH INНERENТ ERRORS // BSU bulletin. Mathematics, Informatics. - 2018. №4. . - С. 58-71.
Title:
IMPROVING ТНЕ ACCURACY OF SOLVING INVERSE PROBLEMS WIТH INНERENТ ERRORS
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-4-58-71UDK: 519.254
Annotation:
Тhе article deals with the issues related to the staЬility of inverse proЫems solution with respect to the exact setting of boundary conditions. 1n practical applications, as а rule, the theoretical form of the boundary conditions functional dependence is unde­ fined or unknown, and there are random measurement eпors. Studies have shown that this leads to а significant decrease in the accuracy of the inverse proЫem solution. 1n order to improve the accuracy of solving inverse proЫems, it was proposed to refine the functional form of the boundary conditions using the recognition of the form of the mathematical model of dependence with the subsequent approximation of the behavior of а physical quantity at the boundary Ьу this function. Restoration of the dependence form is performed Ьу the recognition method based on the reverse display. We have given the model examples of implementation in the presence of additive random meas­ urement eпors and an unknown form ofboundary conditions dependence.
Keywords:
inverse proЫem; recognition; functional dependence; model; inverse function; sampling; variance; approximation.
List of references:
lvanov V. К. , Vasin V. V., Tanana V. Р. Teoriya lineinykh nekorrektnykh zadach i ее prilozheniya [Theory of Linear Ill-posed ProЫems and lts Applications]. Moscow: Nauka РuЫ., 1978. 208 р.

Serebryanskii S. М. ОЬ otsenkakh pogreslmosti metodov priЫizhennogo resheniya odnoi obratnoi zadachi [On Estimation of Errors in Methods for Approxi­ mate Solution of One lnverse ProЫem]. Siblrskii zhurnal industrialnoi matematiki - Journal of Applied and lndustrial Mathematics. 2010. No. 2 (42). Рр. 135-148. 2010. No. 2(42). Рр. 135-148.

Nalimov V. V. Teoriya eksperimenta [Theory of Experiment]. Moscow: Nauka РuЫ., 1971. 208 р.

Aivazyan S. А, Enyukov 1. S., Meshalkin L. D. Prikladnaya statistika: lssledo­ vanie zavisimostei [Applied Statistics: А Study of Dependencies]. Moscow: Finansy i statistika РuЫ., 1985. 487 р.

Кleiner G. В., Smolyak S. А Ekonometricheskie zavisimosti: printsipy i metody postroeniya [Econometric Dependences: Principles and Methods of Construction]. Moscow: Nauka РuЫ., 2000. 104 р.

Orlov А 1. Prikladnaya statistika [Applied Statistics]. 2nd ed., revised and enlarged. Moscow: Ekzamen РuЫ., 2007. 671 р.

Tyrsin А N., Serebryanskii S. М. Raspoznavanie tipa zavisimosti na osnove obratnogo otobrazheniya [Recognition of the Dependency Туре Based on lnverse Dis­ play]. lnformatika i ее primeneniya - Computer Science and lts Applications. 2016. V. 10. lss. 2. Рр. 58--64.

Tikhonov А N. ОЬ ustoichivosti obratnykh zadach [On StaЬility of lnverse ProЫems]. Doklady Academii nauk SSSR - Proceedings of the USSR Academy of Sci­ ences. 1943. V. 39. No. 5. Рр. 195-198.

Tanana V. Р. Metody resheniya operatornykh uravnenii [Methods for Solving Operator's Equations]. Moscow: Nauka РuЫ., 1981. 160 р.

Tanana V. Р., Yaparova N. М. ОЬ optimalnykh ро poryadku metodakh resheniya uslovno-korrektnykh zadach [On Order-of-Magnitude Optimal Solutions of Conditionally Well-Posed ProЫems]. Siblrskii zhumal vychislitelnoi matematiki - Numerical Analysis and Applications. 2006. V. 9. No. 4. Рр. 353-368.