On the formulation of inverse problems

  • Yurii Menshikov
Keywords: INVERSE PROBLEMS, FORMULATION, SYNTHESIS, RECOGNITION

Abstract

Some possible options for the formulation of inverse problems are considered. The ultimate research goals in these cases determine the algorithms for the approximate solution of the inverse problem and allow one to correctly interpret these solutions. Two main statements of inverse problems considered: inverse problems of synthesis and inverse problems of measurement. It is shown that in inverse synthesis problems one should not take into account the error of the mathematical model. In addition, it is possible in these cases to synthesize approximate solution algorithms that do not have a regularizing property. Examples of practical problems considered.

References

Yu.L.Menshikov. Criteria for estimation the adequacy of mathematical descriptions of physical processes // Chapter, Modeling and Simulation in Engineering, Intech-Open, London, 2019, 19p.

Н.Н. Kрасовский, Теория управления движением, Наука, Москва, 1968, –478стр.

А.Н.Тихонов, В.Я.Арсенин. Методы решения некорректных задач. М.; Наука, 1972, 184 стр.

Е.А.Гребеников, Ю.А.Рябов. Поиски и открытия планет. М.: Наука, 1984. -224 с.

V. Chandola, A. Banerjee and V. Kumar, Anomaly detection: A survey, ACM Computing Surveys (CSUR), 41 (2008): l5: l –15:58.

Yu.L.Menshikov. One approach to solutions of measurement's inverse problems // Journal Mathematical Inverse Problems, Vol.1, No.2, 2014, USA, р.71-85.

Published
2020-03-24
Section
Статті